a bicycle racer sprints at the end of a race to clinch a victory. the racer has an initial velocity of 11.5 m/s when he was 300 m away from the finish line. he accelerates at the rate of 0.500 m/s/s for 7.00 s; and then the racer continues at the final velocity to the finish line. (a) what is his final velocity?
As a result, the racer's final velocity is 13.00 m/s after accelerating at 0.500 m/s2 for 7.00 s.
What is velocity?Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s). The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change.
Here,
The final velocity can be found using the equation of motion,
vf = vi + at,
where vf is the final velocity, vi is the initial velocity (11.5 m/s), a is the acceleration (0.500 m/s^2), and t is the time for which the acceleration was applied (7.00 s).
Substituting the values we get,
vf = 11.5 + 0.500 * 7.00 = 13.00 m/s.
So, the racer's final velocity is 13.00 m/s as he accelerates at the rate of 0.500 m/s2 for 7.00 s.
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why would negative initial velocity equal final velocity of the ball at the maximum range of the ball?
Answer:
Negative initial velocity doesn't equal the final velocity of the ball at the maximum range of the ball.
The final velocity of the ball at the maximum range is equal to zero, since at that point the ball has reached its highest point and is no longer moving upward, it is now moving downward.
In physics, when an object is launched upward, its initial velocity is positive and it slows down as it reaches the highest point, then its velocity becomes negative as it starts to fall. The final velocity of the object is zero at the highest point as it is no longer moving upward and it's not yet moving downward.
In the case of a ball being thrown, it's initial velocity is positive when it's thrown, and it slows down as it reaches the highest point, then it's final velocity is zero at the highest point and negative when it starts to fall.
A small engine causes a 2-kg model car to accelerate at a rate of 5m/s2. What is the net force on the model car
Answer:
10N
Explanation:
ΣF = ma
ΣF = (2kg)(5m/s^2)
ΣF = 10N
A rock of mass 2.0 kg is dropped from rest from the top of a house.
When it hits the ground, it has 225 J of kinetic energy.
Calculate the height of the house.
Answer:
Explanation:
Given:
m = 2.0 kg
Wk = 225 J
__________
H - ?
Wp = m*g*H
Wp = Wk
m*g*H = 225
H = 225 / (m*g) = 225 / (2.0*9.8) ≈ 11,5 m
What does the pneumotachograph measure and and how does it measure it?
A pneumotachograph is a device that measures airflow during human or animal respiration. It specifically measures the amount of air that moves into and out of the lungs per unit of time, which is known as the respiratory flow rate.
The pneumotachograph measures the pressure difference across a flow restrictor in the respiratory circuit. The restrictor creates an obstruction in the airflow, resulting in a pressure drop that can be measured. The pneumotachograph can calculate the flow rate of air by measuring the pressure difference and knowing the characteristics of the flow restrictor.
Typically, a flow restrictor is made up of a series of screens or grids with small openings through which air must pass. Turbulence is created as air flows through these openings, which can be measured to determine flow rate.
In clinical settings, pneumotachographs are commonly used to assess respiratory function in patients with lung diseases or other respiratory conditions. In addition, they are used in research settings to investigate respiratory physiology and the effects of various interventions on respiratory function.
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A ball rolls horizontally off the top of a stairway with a speed of 1.52 m/s. the steps are 20.3 cm high and 20.3 cm wide. which step does the ball hit first?
The ball hits the first step and partially lands on it when rolling horizontally off the top of the stairway.
To determine which step the ball hits first, we can analyze the motion of the ball in both the horizontal and vertical directions.
Initial horizontal velocity (Vx) = 1.52 m/s
Step height (h) = 20.3 cm = 0.203 m
Step width (w) = 20.3 cm = 0.203 m
We can calculate the time it takes for the ball to fall vertically by using the equation:
h = (1/2) * g * t^2
where:
g is the acceleration due to gravity (approximately 9.8 m/s²)
t is the time of flight
Rearranging the equation, we have:
t = √(2h/g)
t = √(2 * 0.203 m / 9.8 m/s²)
t ≈ 0.2 s
Now, we can determine the horizontal distance traveled by the ball during this time:
Horizontal distance (d) = Vx * t
d = 1.52 m/s * 0.2 s
d = 0.304 m
Since each step is 0.203 m wide, we can divide the horizontal distance by the step width to determine the step number:
Step number = d / w
Step number = 0.304 m / 0.203 m
Step number ≈ 1.5
Since the step number is not a whole number, we can conclude that the ball hits the first step partially, then continues to the second step. Therefore, the ball hits the first step and partially lands on it.
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Find the center of mass of the region bounded by y=9-x^2 y=5/2x , and the z-axis. Center of Mass = __?
Note: You can earn partial credit on this problem.
The centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8). Formulae used to find the centre of mass are as follows:x bar = (1/M)*∫∫∫x*dV, where M is the total mass of the system y bar = (1/M)*∫∫∫y*dVwhere M is the total mass of the system z bar = (1/M)*∫∫∫z*dV, where M is the total mass of the systemThe region bounded by y=9-x^2 and y=5/2x, and the z-axis is shown in the attached figure.
The two curves intersect at (-3, 15/2) and (3, 15/2). Thus, the total mass of the region is given by M = ∫∫ρ*dA, where ρ = density. We can assume ρ = 1 since no density is given.M = ∫[5/2x, 9-x^2]∫[0, x^2+5/2x]dAy bar = (1/M)*∫∫∫y*dVTherefore,y bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]y*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]ydA...[1].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore,y bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]y*dxdy...[2].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.Substituting the values and evaluating the integral, we get y bar = (1/M)*[(9-5/2)^2/2 - (9-(15/2))^2/2]= (1/M)*(25/2)...[3].
Also, the x coordinate of the center of mass is given by,x bar = (1/M)*∫∫∫x*dVTherefore,x bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]x*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]xdA...[4].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore, x bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]xy*dxdy...[5].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.
Substituting the values and evaluating the integral, we get x bar = (1/M)*[63/8]= (1/M)*(63/8)...[6]Thus, the centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8).
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If the force to stretch a spring is given as k = (100N/m), then what is the potential energy of the spring if it is stretched 1 meters from rest?
Answer:
50 Joules
Explanation:
A 3. 03 kg block is pushed along a horizontal floor by a force F of magnitude 22. 0 N at a downward angle θ=40. 0∘. The coefficient of kinetic friction between the block and the floor is 0. 240. Calculate the magnitudes of (a) the frictional force on the block from the floor and (b) the block's acceleration. (a) Number Units (b) Number Units
The magnitudes of (a) the frictional force on the block from the floor is 7.14 N and (b) the block's acceleration is 3.19 m/s².
The first step to solving this problem is to determine the components of the force F. Since the force is given at an angle, we need to find its horizontal and vertical components.
To find the horizontal component, we use the equation Fx = F xcos(theta), where Fx represents the horizontal component and theta is the angle given (40.0 degrees). Plugging in the values, we get Fx = 22.0 N x cos(40.0 degrees) = 16.83 N.
To find the vertical component, we use the equation Fy = F x sin(theta), where Fy represents the vertical component. Plugging in the values, we get Fy = 22.0 N x sin(40.0 degrees) = 14.16 N.
Next, we need to calculate the frictional force on the block. The formula for the frictional force is Ffriction = coefficient of friction * normal force. The normal force is the force exerted by the floor on the block, which is equal to the weight of the block since it is on a horizontal surface. The formula for the weight is weight = mass * gravity. Plugging in the values, we get weight = 3.03 kg x9.8 m/s². = 29.74 N. Therefore, the normal force is equal to the weight, which is 29.74 N.
Plugging in the values for the coefficient of friction (0.240) and the normal force (29.74 N), we can calculate the frictional force using the formula Ffriction = 0.240 x 29.74 N = 7.14 N.
Now, let's calculate the acceleration of the block. The net force acting on the block is equal to the force Fx minus the frictional force (Fnet = Fx - Ffriction). Plugging in the values, we get Fnet = 16.83 N - 7.14 N = 9.69 N.
To find the acceleration, we use Newton's second law, which states that Fnet = mass x acceleration. Rearranging the formula, we can solve for acceleration: acceleration = Fnet / mass. Plugging in the values, we get acceleration = 9.69 N / 3.03 kg = 3.19 m/s².
In conclusion, the magnitudes of (a) the frictional force on the block from the floor is 7.14 N and (b) the block's acceleration is 3.19 m/s².
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You attend a concert and have a seat that is 70 m away from the stage where the sound is produced. How long does it take for the sound to reach your ears? You take a picture with your phone and send it to your friend who could not come to the concert. She lives in a town 45 miles away. How long does it take until she gets the picture on her phone? Please, include the assumptions that you make.
Given:
distance of observer from the sound source, \(s=70~m\)
distance between the source of image information sender and the receiver, \(d=45~miles=72420.48~m\)
Assumptions:
speed of sound, \(v=343~m/s\)
speed of the image information being sent, \(c=3\times 10^8~m/s\) (we assume it to be nearly the speed of light in vacuum)
Solution:
Time taken by the sound to reach the observer:
\(time=\frac{distance}{speed}\)
\(time=70\div 343\)
\(time \approx 0.2~s\)
Time taken by the image to reach the destination:
\(time=\frac{72420.48}{3\times 10^8}\)
\(time=2.4\times 10^{-4}~s\)
heyyyyyyyyyyyyyyyypt2
The tree branch in the preceding problem sags, and the child's feet rest on the ground. If the tension in the rope is reduced to 220 N, what is the value of the normal force being exerted on the child's feet?
The complete question is
A 45-kg child sits on a 3.2-kg tire swing. The tension on the rope is 470 N. The tree branch sags and the child's feet rest on the ground. If the tension in the rope is reduced to 220 N, what is the value of the normal force being exerted on the child's feet?
Answer:
Therefore the Normal force is being exerted on the child's feet is 252.36( 250N).
Explanation:
We are given
mass of child = 45kg
mass of the tire = 3.2kg
g = 9.8 m/s^2
We have the first case in which the tire is in swing so tension in that case will be which is the resultant force.
Fr = Resultant force
Ft = Tension force
Fg= Gravitational force
Fr = Fg + Ft
0 = -mg + Ft
Ft = mg
= (45+3.2)*9.8
= 48.2 * 9.8
Ft = 472.36N ( which is close to 470)
In the second case the child is in the rest position, The resultant force will be zero.
Fr = Ft + Fn + Fg ( Normal force is denoted by Fn )
0 = Ft + Fn + Fg
Fn = -Fg -Ft
Fn = mg -Ft
= 472.36 - 220
Fn = 252.36N ( close to 250N)
Therefore the Normal force being exerted on the child's feet will be 252.36N.
Imagine that you have an isotropic magnetized plasma with T ∥0
=T ⊥0
=T 0
. Double the magnetic field slowly compared to a gyroperiod, but fast compared to the energy transfer time between T ∥
and T ⊥
. What are the new values of T ∥
and T ⊥
(call them T ∥1
and T ⊥1
) ? Now let the plasma sit long enough for T ∥1
and T ⊥1
to mix by collisions and come to an isotropic temperature T 1
, but not long enough for the plasma to exchange energy with the outside world. What is T 1
? Reduce the magnetic field back down to its original value slowly compared to a gyroperiod, but fast compared to the energy transfer time between T ∥
and T ⊥
. What are T ∥2
and T ⊥2
? And after the plasma becomes isotropic, what is T 2
? This process is called 'magnetic pumping'.
The new values of T∥1 and T⊥1 will be equal to the original isotropic temperature T0.
When the magnetic field is doubled slowly compared to a gyroperiod but fast compared to the energy transfer time between T∥ and T⊥, the plasma remains magnetized, but the magnetic field becomes stronger. Since the energy transfer time between T∥ and T⊥ is much longer than the timescale of magnetic field doubling, the temperature anisotropy is not affected during this process. Therefore, T∥1 and T⊥1 remain equal to T0.
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Consider a situation where you are playing air hockey with a friend. The table shoots small streams of air upward to keep the puck afloat and to minimize friction. When you barely tap the puck forward, it.
It will move with a constant speed until hitting the other end
When we hit the puck from tap the puck will move forward.
This is because of the impulse that we gave at the moment of the hit. This impulse causes the puck to advance and begin traveling in a particular direction.
The air stream force balances the weight of the puck, so as soon as it moves forward, there is no longer any force acting on it. The puck will continue moving forward until it collides with another object.
Until it collides with some other points, the puck will move consistently.
So, in this case, the appropriate response will be
until it reaches the opposite end, it moves at a constant speed.
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synchronous satellite, which always remains above the same point on Earth’s equator, is put in circular orbit around Earth. Earth rotates once every 24 hours. Find the altitude of the satellite.
The altitude of the synchronous satellite is approximately 35,786 kilometers.
To determine the altitude of the synchronous satellite, we need to consider that it always remains above the same point on Earth's equator.
This means that the satellite completes one orbit around the Earth in the same time it takes for the Earth to complete one rotation, which is 24 hours.
Using the formula for the period of a circular orbit, T = 2π√(a³/GM), where T is the period, a is the altitude, G is the gravitational constant, and M is the mass of the Earth, we can solve for a.
Substituting the known values and simplifying, we get:
24 hours = 2π√[(a + 6378 km)³/(6.67 x 10^-11 Nm²/kg² x 5.97 x 10^24 kg)]
Solving for a, we get a value of approximately 35,786 kilometers. Therefore, the altitude of the synchronous satellite is approximately 35,786 kilometers.
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A car accidentally rolls down a driveway for 8.0m while a person pushes agqinst the car with a foce 850 N to bring it to a stop. What is the change in kinetic energy for the car?
Given what we know, we can confirm that the change in kinetic energy is a negative value, given that the final value will be zero.
What is kinetic energy?This is the energy of movement.As the car is in motion, it has kinetic energy. However, as the car slows down, it loses this energy. Once the car stops, it no longer has kinetic energy. Given that the change in kinetic energy is the final value minus the initial, and the final is zero, this will cause the change in kinetic energy for the car to be a negative value.Therefore, since kinetic energy is the energy of movement, we can confirm that the change in kinetic energy for the car will be a negative value caused by the car coming to a complete stop.
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A car accidentally rolls down a driveway for 8.0 m while a person pushes against the car with a force of 850 N to bring it to a stop.
What is the change in kinetic energy for the car?
Answer: -6800 J
WILL MARK BRAINALIST PLS HELP
In which situation is no work considered to be done by force?
A.) when the angle between the force and displacement is 180°
B.) when the angle between the force and displacement is 90°
C.) when the angle between the force and displacement is 45°
D.) When the angle between the force of displacement of 0°
Answer:
B.) when the angle between the force and displacement is 90°
Explanation:
what is the voltage across the inductor in the instant just after the switch is closed? use the following data: vb = 8.10, v; r = 147.0 ωω; l = 5.65×10-1 h.
The voltage across the inductor just after the switch is closed can be calculated using the following data: V b = 8.10 V, R = 147.0 Ω, and L = 5.65×10^-1 H.
Explanation:
Step 1: Calculate the initial current (I0) through the circuit when the switch is closed. Since the inductor acts as a short circuit in the instant just after the switch is closed, the initial current can be calculated using Ohm's Law:
I0 = Vb / R
Step 2: Calculate the voltage across the inductor (VL) just after the switch is closed using the initial current (I0) and the inductor value (L):
VL = L * (dI/dt)
Since the inductor acts as a short circuit just after the switch is closed, the rate of change of current (dI/dt) is infinite. Therefore:
VL = L * ∞
In conclusion, the voltage across the inductor just after the switch is closed is infinite due to the inductor acting as a short circuit and the rate of change of current being infinite.
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Is it correct to conclude that one engine is doing twice the work of another just because it is generating twice the power? Explain.
Answer:
It is not correct to conclude that one engine is doing twice the work of another just because it is generating twice the power. If one engine generates twice the power as the other, it may be generating the same amount of work in one half of the time.
Explanation:
It is not correct that the engine generating more power is doing more work. Because it is the time that differ between engines. The engine which generates twice power is completing the work within half time taken by the other engine.
What is power?Power is the rate of work done. When a force result in displacement of an object, it said to be work done on the object. The work done is a vector quantity and it is characterised by its magnitude and direction similar to the force.
Power is the ratio of change in work done to the change in time. Therefore, the more work done in a small time interval create the greater power.
The engine which is producing a power twice comparison to the other is completing the work in half of the time taken by the other engine. But, both might be doing the amount of work. Hence, the statement is wrong.
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BRAINLIEST! I NEED HELP ASAP!
The ratio of xi to xo for a certain mirror is 2.5. Which is true of an image produced by this mirror?
It is 2.5 times larger and virtual.
It is 2.5 times larger and real.
It is 2.5 times smaller and virtual.
It is 2.5 times larger and real.
The true of an image produced by this mirror will be 2.5 times smaller and virtual. Option C is correct.
What is the image?When light beams from an object reflect off a mirror, they intersect with the picture of that thing called an image. Real and virtual images are the two sorts of images.
The ratio of xi to xo for a certain mirror is 2.5;
\(\rm \frac{x_i}{x_0} =2.5 \\\ x_i=2.5 x_0\)
Where,
\(\rm x_0\) is the true of an image produced by this mirror.
The true of an image produced by this mirror will be 2.5 times smaller and virtual.
Hence,option C is correct.
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When a runner hits the ball and makes it around all bases safely to Home Base without getting tagged out it is called a?
Answer:
Home run
Explanation:
i play
can someone pls help with the last one
Answer:
ummmmmmmmmmmm ask your teacher or perant for help
Explanation:
so umm ask an adult or teen figure and maybe you will get it write not sure do
A 4.0 kg object will have a weight of approximately 14.8 N on Mars. What is the gravitational field strength on M
Answer:
Gravitational field strength =weight/mass
Explanation:
14.8N/4.0kg
3.7N/kg
What main factor determines the stages a star will follow after the main sequence?.
The main factor that determines the stages of a star after the main sequence is the star mass. Depending on the mass, stars will develop as average stars -low mass- or giant stars -high mass-.
How does the star evolution -star cycle- occur?
The star cycle is the sequence of changes that a star undergoes throughout its existence
Stars are born from the nebula, which is dust and gas particles condensation due to the gravity effect in the interstellar clouds.
These stellar clouds collapse and compose smaller regions, each of which later contracts and compose the stellar cores. This is a more advanced level of condensation.
Stelar cores are protostars that contract and increase their temperature until nuclear reactions occur. Hydrogen is converted into Helium and the new star gets born.
This new star is in its main sequence, which is the equilibrium point between gravity and nuclear fusion, which helps the star keeps stable as long as the fuel lasts.
Stars spend most of their lives in the main sequence until all hydrogen turns into helium and there is no more fuel left.
At this point, the star is a subgiant, and its core begins its contraction, increasing the star's temperature.
The star increases in size and luminosity, turning into a giant.
After the subgiant stage, the star enters a giant phase. The star can reach a size up to 100 times its current size.
When the core reaches a certain temperature, helium turns into carbon.
The following events depend on the star mass.
Star < 8 solar masses ⇒ the star turns into a white dwarf
When average-sized stars run out of fuel, the red giant begins to disintegrate, losing its outer layers and exposing its core, which will become a white dwarf.
Star > 8 solar masses ⇒ the star turns into a supernova/neutron star.
When fuel is over in the star, the gravitational collapse produces an explosion originating the supernova.
This neutron star is a celestial body that remains as a remnant after the explosion giving rise to a supernova.
In these cases, if the star core has a mass > 3 solar masses, the star collapses into a black hole.
In conclusion, the main factor that determines the stages a star follows after the main sequence is the star mass. Depending on the mass, stars will develop as average stars -low mass- or giant stars -high mass-.
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A model rocket with no parachute is launched vertically from rest with an acceleration of 15 m/s
2
. The rocket reaches a maximum velocity of 60 m/s before the engine shuts off. What height is the rocket when the velocity is at its greatest? What is the maximum height off of the ground that the rocket reaches? How long is the rocket airborne (How much time elapses before the rocket hits the ground?)?
A. The height of the rocket when the velocity is at its greatest is 120 m
B. The maximum height reached is 183.67 m
C. The time taken to hit the ground is 12.24 s
A. How do i determine the height at the greatest velocity?The height reached when the velocity is greatest can be obtained as follow:
Initial speed (u) = 0 m/sFinal speed (v) = 60 m/s Acceleration (a) = 15 m/s²Height (h) =?v² = u² + 2ah
60² = 0² + (2 × 15 × h)
3600 = 0 + 30h
Collect like terms
30h = 3600
Divide both sides by 30
h = 3600 / 30
= 120 m
B. How do i determine the maximum height reached?The maximum height reached can be obtained as follow:
Initial speed (u) = 60 m/sFinal speed (v) = 0 m/s Acceleration due to gravity (g) = 9.8 m/s²Maximum height (h) =?v² = u² - 2gh
0² = 60² - (2 × 9.8 × h)
0 = 3600 - 19.6h
Collect like terms
19.6h = 3600
Divide both sides by 19.6
h = 3600 / 19.6
= 183.67 m
C. How do i determine the time in the air?First, we shall obtain the time to reach the maximum height. Details below:
Height (h) = 183.67 mAcceleration due to gravity (g) = 9.8 m/s²Time taken (t) = ?h = ½gt²
183.67 = ½ × 9.8 × t²
183.67 = 4.9 × t²
Divide both side by 4.9
t² = 183.67 / 4.9
Take the square root of both side
t = √(183.67 / 4.9)
t = 6.12 s
Finally, we shall obtain the time in the air. Details below:
Time to reach maximum height (t) = 6.12 sTime in air (T) =?T = 2t
= 2 × 6.12
= 12.24 s
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a cylinder is measured to have a diameter of 3.5 inches, and a length of 5.6 cm. its mass is 1600 grams. calculate its density in kg/m3.
The density of the cylinder is 14100 kg/m³. The result is obtained by using the formula for density.
What is the density of a substance?The density is the mass of a substance per unit of volume. It can be expressed as
ρ = m/V
Where
ρ = densitym = massV = volumeA cylinder is measured to have
Diameter, d = 3.5 inchesLength, l = 5.6 cmMass, m = 1600 gramsFind its density in kg/m³!
The radius of the cylinder is
r = ½d
r = ½(3.5)
r = 1.75 inches
r = 1.75 × 2.54 cm
r = 4.4 cm
We find the volume of the cylinder.
V = ⅓ πr²l
V = ⅓ (3.14))(4.4)²(5.6)
V = 113.5 cm³
The density will be
ρ = m/V
ρ = 1600/113.5
ρ = 14.1 g/cm³
Let's convert the unit of density to kg/m³!
ρ = 14.1 × 1/1000 × 1000000/1 kg/m³
ρ = 14100 kg/m³
Hence, the cylinder has the density of 14100 kg/m³.
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Select ALL THAT APPLY to the following situation.
No work is done when:
an object is lifted straight up off the ground
1 an object stays at rest
an object is moved in the same direction as the force acting on it
an object is moved in a different direction than the forces acting on it
therbligs are: the smallest unit of time used in methods time measurement exercises. the largest unit of time used in methods time measurement exercises. basic physical elements of motion as used in methods time measurement exercises. the full range of motions required to complete a job as used in methods time measurement exercises. the smallest amount of time required to complete a job.
Therbligs are basic physical elements of motion used in methods time measurement exercises to analyze and measure work processes. They represent the smallest unit of time and the full range of motions required to complete a job.
Therbligs were introduced by Frank B. Gilbreth, an industrial engineer, as a means to analyze and improve work processes. They are used in methods time measurement exercises to break down a task or job into its fundamental motions. Each therblig represents a specific basic physical element of motion, such as grasp, position, release, search, transport, and so on. These elements can be combined in different sequences to represent the full range of motions required to complete a job. Therbligs are used to measure the time required to perform each individual motion, and by summing up the times for all therbligs involved, the total time to complete a job can be determined. By analyzing the therbligs involved in a task, engineers can identify inefficiencies, eliminate unnecessary motions, and streamline work processes to increase productivity and reduce fatigue or strain on workers.
Therefore, therbligs serve as a standardized method for measuring and evaluating work processes, allowing for improvements in efficiency and productivity. They represent both the smallest unit of time used in methods time measurement exercises (individual motions) and the largest unit of time (the full range of motions required to complete a job).
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What feature of molecular orbital theory is responsible for bond formation?
Molecular Orbital Theory (MOT) is a key concept in understanding chemical bonding, and it explains the formation of bonds through the interaction of atomic orbitals. The essential feature of MOT responsible for bond formation is the concept of constructive and destructive interference between the overlapping atomic orbitals.
When two atoms approach each other, their atomic orbitals overlap and combine to form molecular orbitals. These molecular orbitals can be bonding or antibonding, depending on the nature of their interaction. Constructive interference occurs when the wave functions of the atomic orbitals combine in-phase, resulting in a lower energy molecular orbital with electron density concentrated between the nuclei. This increased electron density strengthens the electrostatic attraction between the positively charged nuclei and the negatively charged electrons, forming a stable chemical bond.
On the other hand, destructive interference occurs when the wave functions of the atomic orbitals combine out-of-phase, leading to the formation of a higher energy antibonding molecular orbital. In this case, electron density is reduced between the nuclei, creating a node that weakens the electrostatic attraction and destabilizes the bond. Electrons in antibonding orbitals can counteract the bonding effect of electrons in bonding orbitals.
Bond order, a measure of bond strength, is determined by the difference between the number of electrons in bonding and antibonding orbitals. A positive bond order signifies a stable bond, while a zero or negative bond order indicates that the bond is not formed or is weak.
In summary, the formation of molecular orbitals through constructive and destructive interference between atomic orbitals is the key feature of MOT responsible for bond formation. Bonding orbitals result in stable chemical bonds, while antibonding orbitals can weaken or prevent bonds from forming.
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A 221-gram ball is thrown at a speed of 36.7 m/s from the top of a 39.8-m high cliff. Determine the impact speed of the ball when it strikes the ground. Assume negligible air resistance.
Given:
The mass of the ball is
\(\begin{gathered} m=221\text{ g} \\ =0.221\text{ kg} \end{gathered}\)The initial height of the ball is
\(h=39.8\text{ m}\)The initial speed of the ball is
\(v_i=36.7\text{ m/s}\)To find:
the impact speed of the ball when it strikes the ground
Explanation:
The initial potential energy of the ball is
\(\begin{gathered} (PE)_i=mgh \\ =0.221\times9.8\times39.8 \\ =86.2\text{ J} \end{gathered}\)The initial kinetic energy is
\(\begin{gathered} (KE)_i=\frac{1}{2}mv_i^2 \\ =\frac{1}{2}\times0.221\times(36.7)^2 \\ =148.8\text{ J} \end{gathered}\)The final energy of the ball is fully kinetic energy. Let the final impact speed of the ball is
\(v_f\)We can write, using the energy conservation principle that
\(\begin{gathered} (PE)_i+(KE)_i=\frac{1}{2}mv_f^2 \\ 86.2+148.8=\frac{1}{2}\times0.221\times v_f^2 \\ v_f^2=2\times\frac{86.2+148.8}{0.221} \\ v_f=46.1\text{ m/s} \end{gathered}\)Hence, the final impact speed of the ball is 46.1 m/s.