Answer:
9000 J
Explanation:
Convert minutes to seconds.
2 min = 120 s
Power = energy / time
75 W = E / 120 s
E = 9000 J
As you look at the side of the wheel, you can see it spinning clockwise. What are the directions of the angular velocity, and angular momentum?
If the torque is applied to the rim, causing the wheel to slow down, what are the directions of the torque and the angular acceleration?
Answer:
The direction of angular velocity and angular momentum are perpendicular to the plane of rotation. Using the right hand rule, the direction of both angular velocity and angular momentum is defined as the direction in which the thumb of your right hand points when you curl your fingers in the direction of rotation.
Explanation:
If an object has a mass of 2 g and a volume of 7 cm3, what is its density?
The density of an object whose mass is 2 g and volume is 7 cm³ is 0.285 g/cm³
What is the relation between the mass and density of a solid body?
The mass and density of any substance are related as follows -
M = ρ × V
Where -
[M] - mass of substance
[ρ] - density of substance
[V] - volume of substance
Given is an object that has a mass of 2 g and a volume of 7 cm³.
We know that the relation between mass and density is -
M = ρ × V
Mass [M] = 2 gram
Volume [V] = 7 cm³
Substituting the values, we get -
2 = ρ x 7
ρ = 2/7
ρ = 0.285 g/cm³
Density of the object is 0.285 g/cm³
Therefore, the density of an object whose mass is 2 g and volume is 7 cm³ is 0.285 g/cm³
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6. Describe why field investigations can differ from classroom experiments.
Field investigations and classroom experiments can differ in several ways due to the unique characteristics and limitations of each setting.
Here are some reasons why field investigations can differ from classroom experiments:Real-world context: Field investigations take place in the natural environment, allowing students to observe and study phenomena in their natural setting. This context provides a more authentic experience and helps students understand the complexities and interactions of the real world. In contrast, classroom experiments often involve controlled conditions that may not accurately reflect real-world scenarios.Complexity and unpredictability: Field investigations often deal with complex and unpredictable variables, such as weather, terrain, and natural processes. This complexity can make it challenging to control and manipulate variables compared to classroom experiments, where conditions can be tightly controlled.Scale and scope: Field investigations can involve larger scales and broader scopes than classroom experiments. For example, studying the ecosystem of a forest or the geological features of a landscape requires observing and collecting data over a large area, which may not be feasible within a classroom setting.Resources and equipment: Classroom experiments often have access to a controlled and well-equipped laboratory, whereas field investigations may require specialized equipment, transportation, and logistical planning to conduct research in the field. This can add logistical challenges and resource constraints to field investigations. Ethical considerations: Field investigations may involve interactions with living organisms and ecosystems, raising ethical considerations related to environmental impact and the well-being of organisms. Classroom experiments, on the other hand, can be designed with ethical considerations in mind, ensuring the well-being and safety of participants.Overall, field investigations provide students with valuable opportunities to engage with the natural world, understand its complexity, and develop skills in observation, data collection, and critical thinking. Classroom experiments, on the other hand, offer controlled environments for testing specific hypotheses and concepts. Both approaches have unique benefits and play important roles in science education, providing complementary learning experiences for students.
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A 1.2-kg mass is projected from ground level with a velocity of 31.3 m/s at some unknown angle above the horizontal. A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence
Answer:
The kinetic energy will be "399.65 J".
Explanation:
Given:
Mass,
m = 1.2 kg
Velocity,
v = 31.3 m/s
The total energy of mass will be:
⇒ \(E=K+U\)
or,
⇒ \(E=.5mv^2+mgh\)
By putting the values, we get
\(=.5(1.2)(31.3)^2+0\)
\(=0.6\times 979.69+0\)
\(=587.81 \ J\)
Since,
The system's total energy is unchanged, then
⇒ \(E=K+U\)
or,
⇒ \(E=K+mgh\)
\(587.81=K+1.2(9.8)(16)\)
\(587.81=K+188.16\)
\(K=587.81-188.16\)
\(=399.65 \ J\)
An object traveling at a constant
angular speed requires 4.0 seconds
to make one complete revolution.
What is its angular speed?
rad
S
Answer:
pi / 2 radians / s
Explanation:
One revolution = 2 pi Radians in 4 seconds
2 pi / 4 = pi/2 radians / s
4. A marble is rolled off a table that is 2 m high with an initial velocity of 3 m/s. If an identical marble is rolled horizontally off the same table at a velocity of 6 m/s, what happens to the falling time? (Hint: Use your other analysis questions to help you answer) (1 point)
Answer ___________________
Choices:
A. Flight time is doubled. C. Flight time is cut in half.
B. Flight time is the same. D. Flight time is exponentially increased.
Answer:
the correct statement is B Flight time is the same.
Explanation:
This is a projectile launch problem, in this case as it is rolling on a horizontal table all the initial horizontal velocity, for the time it takes to reach the floor we use
y =\(y_{o}\) I + \(v_{oy}\) t - ½ g (t-t₀)
get to the floor y = 0
0 =y_{o} - ½ g (t-t₀)²
t = t₀ + √ (2 y_{o}/ g)
we see that the time to delegate to the floor does not depend on the initial velocity m for which the time to reach the floor is the same, regardless of the velocity of the body
the correct statement is B Flight time is the same.
A 20 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and slides away from the wall at a rate of 2ft/sec. Find the velocity of the top of the ladder at time t=1.
Answer: 0.516 ft/s
Explanation:
Given
Length of ladder L=20 ft
The speed at which the ladder moving away is v=2 ft/s
after 1 sec, the ladder is 5 ft away from the wall
So, the other end of the ladder is at
\(\Rightarrow y=\sqrt{20^2-5^2}=19.36\ ft\)
Also, at any instant t
\(\Rightarrow l^2=x^2+y^2\)
differentiate w.r.t.
\(\Rightarrow 0=2xv+2yv_y\\\\\Rightarrow v_y=-\dfrac{x}{y}\times v\\\\\Rightarrow v_y=-\dfrac{5}{19.36}\times 2=0.516\ ft/s\)
Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In a typical strike, the chameleon's tongue accelerates at a remarkable 220 m/s^2 for 20 msms, then travels at constant speed for another 30 ms.
Required:
During this total time of 50 ms, 1/20 of a second, how far does the tongue reach?
Solution :
We know,
Distance,
\($S=ut+\frac{1}{2}at^2$\)
\($S=ut+0.5(a)(t)^2$\)
For the first 20 ms,
\($S=0+0.5(220)(0.020)^2$\)
S = 0.044 m
In the remaining 30 ms, it has constant velocity.
\($v=u+at$\)
\($v=0+(220)(0.020)\)
v = 4.4 m/s
Therefore,
\($S=ut+0.5(a)(t)^2$\)
\($S'=4.4 \times 0.030\)
S' = 0.132 m
So, the required distance is = S + S'
= 0.044 + 0.132
= 0.176 m
Therefore, the tongue can reach = 0.176 m or 17.6 cm
Answer:
The total distance is 0.176 m.
Explanation:
For t = 0 s to t = 20 ms
initial velocity, u = 0
acceleration, a = 220 m/s^2
time, t = 20 ms
Let the final speed is v.
Use first equation of motion
v = u + at
v = 0 + 220 x 0.02 = 4.4 m/s
Let the distance is s.
Use second equation of motion
\(s = u t + 0.5 at^2\\\\s = 0 + 0.5 \times 220 \times 0.02\times 0.02\\\\s = 0.044 m\)
Now the distance is
s' = v x t
s' = 4.4 x 0.03 = 0.132 m
The total distance is
S = s + s' = 0.044 + 0.132 = 0.176 m
If a student weighs 100 pounds on Earth, how much more or less would she weigh on Pluto than Mars?
A. She would weigh 38 pounds less on Pluto
B. She would weigh 38 pounds more on Mars
C. She would weigh 31 pounds more on Mars
D. She would weigh 31 pounds less on Mars
Answer:
c because that's the answer
She would weigh 31 pounds more on Mars than on Pluto. Therefore option C is correct.
To calculate the differences in weight using the given information.
1. Weight on Earth: 100 pounds
Now, let's calculate the weight differences for Pluto and Mars:
2. Weight on Pluto:
Pluto's gravity is about 0.06 times that of Earth's.
Weight on Pluto = Weight on Earth × Pluto's gravity
Weight on Pluto = 100 pounds × 0.06 = 6 pounds
3. Weight on Mars:
Mars' gravity is about 0.38 times that of Earth's.
Weight on Mars = Weight on Earth × Mars' gravity
Weight on Mars = 100 pounds × 0.38 = 38 pounds
Comparing the weight differences:
Weight difference between Earth and Pluto = 100 pounds - 6 pounds = 94 pounds
Weight difference between Earth and Mars = 100 pounds - 38 pounds = 62 pounds
Therefore, the correct answer is C. She would weigh 31 pounds more on Mars than on Pluto.
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In hiking, what fitness component is required of you
To better understand crash dynamics we have to look at "__________."
A. the law of gravity
B. Bernoulli's principle
C. the laws of motion
D. Archimedes' principle
To better understand crash dynamics we have to look at "the laws of motion."
The laws of motion
The laws of motion were introduced by Sir Isaac Newton in 1687 in his book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), which defined the laws of motion, or three fundamental laws that govern the movement of bodies. The laws of motion, according to Newton, govern the motion of an object or a system of objects that interact.
It defines the concepts of force and mass, and the fundamental dynamics of motion.The following are the laws of motion:Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. The velocity of an object changes proportional to the force applied to it, and the acceleration of an object is proportional to both its force and its mass. For every action, there is an equal and opposite reaction.
Therefore, these laws are necessary to fully grasp crash dynamics because they explain how objects respond to outside forces that cause them to accelerate or decelerate.
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The carts are moving on a level, frictionless track. After the collision all three carts stick together. Find the speed of the combined carts after the collision.
Answer:
0.13 m/s
Explanation:
Unfortunately, I don't have an explanation but I guessed the correct answer.
Can positive charges be liberated by the photoelectric effect?
yes
rarely
no
sometimes
Answer:
No, positive charges cannot be liberated by the photoelectric effect.
Explanation:
A spatially challenged goldfish swims along the x-axis only. Its initial position is 7.8 m. After swimming back and forth a while, it finds itself at the position 4.4 m. Calculate the fish’s displacement (including its sign).
Answer:
The fish displacement was -3.4 m
Explanation:
Distance and Displacement
A moving object constantly travels some distance at defined periods of time. The total moved distance is the sum of each individual distance the object traveled. It can be written as:
dtotal=d1+d2+d3+...+dn
This sum is obtained independently of the direction the object moves.
The displacement only takes into consideration the initial and final points of the path defined by the object in its moving. The displacement, unlike distance, is a vectorial magnitude and can be even zero if the object starts and ends the movement at the same point.
The displacement, when the object moves in one axis only is given by:
d = final position - initial position
We know the fist started at 7.8 m from a given reference along the x-axis.
After some undisclosed movements, it ends up at the position 4.4 m. Thus, the displacement is:
d = 4.4 m - 7.8 m = -3.4 m
This means the fish ended up to the left of the position it started from.
The fish displacement was -3.4 m
A man has to push his boat on the shore across the mud to get to the water. The coefficient of friction between the boat and the mud is given by μ = 0.500. If the boat has a mass of 50 kg, calculate the magnitude of the force of friction acting on the boat
The magnitude of the force of friction acting on the boat is 245.25 N.
How do you determine the amount of friction energy being applied to?F = mg sin - kmg cos is the formula for the component of the total force down the slope.
The following algorithm can be used to determine the amount of friction the boat is experiencing:
F friction = friction coefficient * normal force
normal force=weight of the boat
=m *g
where m is the mass of the boat and g is the acceleration due to gravity (9.81 m/s²).
Therefore, the force of friction on the boat is:
F friction = μ * m * g
Substituting the given values, we get:
F friction = 0.500 * 50 kg * 9.81 m/s² = 245.25 N
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Suppose there are 3 molecules in a container. If each molecule has a 1-in-2 chance of being in the left half of the container, what is the probability that there are exactly 2 molecules in the left half of the container?
Answer:
Total probability = 3/8
Explanation:
Below is the calculation:
Number of molecules in the container = 3
The probability of one molecule in the left half, P = 3 / 2 = 1.5 or 1/2
The probability of second molecule in the left half, P1 = (3/4)
Total probability = P x P1
Total probability = (1/2) x (3/4)
Total probability = 3/8
Consider the circuit in Figure 5 with e(t) = 12sin(120pit) V. When S1 and S2 are
open, i leads e by 30°. When SI is closed and S2 is open, i lags e by 30°. When S1 and S2 are closed, i has an amplitude 0.5A. What are R, L, and C?
Based on the information, it should be noted that the resistance R is 0.5 Ω.
How to calculate the resistanceWhen S1 and S2 are open, i leads e by 30°. In this case, the circuit consists of only the inductor (L) and the capacitor (C) in series. Therefore, the impedance of the circuit can be written as:
Z = jωL - 1/(jωC)
Since i leads e by 30°, we can express the phasor relationship as:
I = k * e^(j(ωt + θ))
Z = jωL - 1/(jωC) = j(120π)L - 1/(j(120π)C)
Re(Z) = 0
By equating the real parts, we get:
0 = 0 - 1/(120πC)
Let's assume that there is a resistance (R) in series with the inductor and capacitor. The impedance equation becomes:
Z = R + jωL - 1/(jωC)
Z = R + jωL
Im(Z) = ωL > 0
Substituting the angular frequency and rearranging the inequality, we have:
120πL > 0
L > 0
This condition implies that the inductance L must be greater than zero.
When S1 and S2 are closed, i has an amplitude of 0.5 A. In this case, the impedance is:
Z = R + jωL - 1/(jωC)
Since the amplitude of i is given as 0.5 A, we can express the phasor relationship as:
I = 0.5 * e^(j(ωt + θ))
By substituting this phasor relationship into the impedance equation, we can determine the value of R. The real part of the impedance must be equal to R:
Re(Z) = R
Since the amplitude of i is 0.5 A, the real part of the impedance must be equal to 0.5 A: 0.5 = R
Therefore, the resistance R is 0.5 Ω.
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Which statement best describes the primary difference between scientific investigation and technological design?
Scientific investigation is more time consuming than technological design.
Technological design is more expensive than scientific investigation.
Technological design involves background research, and scientific investigation does not require research.
Scientific investigation involves experiments, and technological design involves products.
Su
The statement best describes the primary difference between scientific investigation and technological design is Scientific investigation involves experiments, and technological design involves products. Option D
What are scientific investigation and technological design?It can be said that both scientific investigation and technolgical design require problem-solving, creativity, and rigorous methods.
However, both of them have different objectives. While Scientific investigation seeks to expand knowledge and understanding of the natural world. Research involvs hypothesis testing and different experiments;
on the other hand, Technological design, wants to create or improve products, processes, or systems to meet specific needs or solve particular problems.
It can then be defined as the application of scientific knowledge for practical purposes.
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Suppose we are told that the position of an object (x) moving with an acceleration a is proportional to some power of a, say an and some power of t, say tm. Determine the values of n and m and write the simplest form of an equation for the position.
(a) The value of n is 1 and the value of m is 2
(b) The simplest form of an equation for the position is \(at^2\)
The given expression:
\(x = a^nt^m\)
To find:
the values of a values of n and msimplest form of the equationThe values of n and m will be calculated using the dimensions of accelerations, position and time.
The dimension of acceleration, \(a = LT^{-2}\)The dimension of position, x = LThe dimension of time, t = T(a) the values of n and m are calculated as follows:
\(x = a^n t^m\\\\ L = [LT^{-2}]^n [T]^m\\\\L = [L]^n [T^{-2n}][T]^m\\\\L = [L]^n[T^{m-2n}]\\\\L^1T^0 = [L]^n[T^{m-2n}]\\\\L^1 = L^n\\\\n = 1\\\\T^0 = T^{m-2n}\\\\0 = m - 2n\\\\0 = m- 2(1)\\\\0 = m- 2\\\\m = 2\)
(b) The simplest form of an equation for the position can be written as;
\(x = a^n t^m\\\\x = a^1 t^2\\\\x = at^2\)
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A racing car has a mass of 1530 kg. What is its kinetic energy if it has a speed of 120 km/h? Assume that air resistance is negligible.
The kinetic energy of the racing car is approximately 849952.4 J joules.
What is its kinetic energy of the car?Kinetic energy is simply a form of energy a particle or object possesses due to its motion.
It is expressed as;
K = (1/2)mv²
Where m is mass of the object and v is its velocity.
Convert the speed from kilometers per hour to meters per second since the units of mass and velocity need to be consistent.
We know that 1 km/h = 0.27777 m/s, so:
120 km/h x (0.27777 m/s/km/h) = 33.3336 m/s (rounded to 4 decimal places)
Now we can substitute the values into the formula:
Kinetic Energy = (1/2) × 1530 kg x (33.3336 m/s)²
Kinetic Energy = 849952.4 J
Therefore, the kinetic energy is approximately 849952.4 joules.
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A transformer has 120 turns on the primary coil and 70 turns on the secondary coil. If the output voltage is 220V, what is the input voltage?
answer : input voltage = 377.143
steps:
Vout/Vin = Ns/Np
p = primary
s = secondary
primary and secondary voltages
are the same as
induced EMF
V is voltage
N is number of turns
output voltage / input voltage = secondary turns / primary turns
220/input voltage = 70 / 120
input voltage * 70 = 220 * 120
input voltage = (220 * 120)/70
input voltage = 377.143
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Socratic
quizlet
The same spring is stretched 5 m. What was the force?
Answer:
La fuerza del resorte es directamente proporcional a la extensión del resorte. En otras palabras, si jalas mucho de la masa, la fuerza será intensa; si jalas poco de la masa, la fuerza será débil.
Explanation:
Butyl carbitol, used in the production of plastics, is stored in a tank having the U-tube manometer. Take SHg = 13.55, Sbc =0.957, and Rho w=1000 kg/m^3. If the U-tube is filled with mercury to level E, determine the gage pressure in the tank at point B.
The gage pressure in the tank at point B is:
Pgage = Patm + Pmano = 1 kPa - 1.01 kPa = -0.01 kPa
Note that the negative sign indicates that the pressure in the tank is lower than atmospheric pressure.
What is Pressure?
Pressure is a measure of the amount of force per unit area applied on a surface. It is defined as the force applied perpendicular to the surface divided by the area of the surface. The SI unit of pressure is the pascal (Pa), which is defined as one newton of force per square meter of area.
To determine the gage pressure in the tank at point B, we need to calculate the height difference between points B and E in the U-tube manometer and then convert this height difference to pressure using the density of mercury.
The height difference between points B and E is given by:
h = Sbc * (h1 - h2)
where Sbc is the specific gravity of butyl carbitol, h1 is the height of the mercury column on the left side of the U-tube, and h2 is the height of the mercury column on the right side of the U-tube. Since the U-tube is filled with mercury to level E, we have:
h1 = h2 = HE
where HE is the height of the mercury column at level E.
Substituting these values, we get:
h = Sbc * (HE - HE) = 0
Therefore, the height difference between points B and E is zero, which means that the pressure at point B is equal to the pressure at point E. The pressure at point E is atmospheric pressure, which we assume to be 1 atm. Therefore, the gage pressure at point B is:
Pgage = Patm + Pmano
where Patm is atmospheric pressure and Pmano is the pressure due to the height of the mercury column above point E. Using the density of mercury (SHg) and the height of the mercury column (HE), we can calculate Pmano as:
Pmano = SHg * g * HE
Substituting the given values, we get:
Pmano = 13.55 * 9.81 * HE
To determine HE, we need to consider the pressure difference between points A and B. Since the U-tube is filled with mercury to level E, the pressure at point A is also atmospheric pressure. Therefore, the pressure difference between points A and B is equal to the gage pressure at point B:
PAB = Pgage = Patm + Pmano
Substituting the given values and solving for HE, we get:
HE = (PAB - Patm) / (SHg * g) = (0 - 1) / (13.55 * 9.81) = -0.00734 m
Note that the negative value of HE indicates that the height of the mercury column on the right side of the U-tube is higher than the height on the left side. This is consistent with the assumption that the gage pressure at point B is negative, which means that the pressure in the tank is lower than atmospheric pressure.
Finally, substituting the calculated value of HE into the equation for Pmano, we get:
Pmano = 13.55 * 9.81 * (-0.00734) = -1.01 kPa
Therefore, the gage pressure in the tank at point B is:
Pgage = Patm + Pmano = 1 kPa - 1.01 kPa = -0.01 kPa
Note that the negative sign indicates that the pressure in the tank is lower than atmospheric pressure.
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state the law of conservation of energy
Answer:
energy can neither be created nor be destroyed. Although, it may be transformed from one form to another.
Explanation:
mark brainiest?
Answer:
According the law of conservation of energy , energy is not created or destroyed
1. What is magnetism?
2. What is electromagnetism?
Answer:
Magnetism is the force or ability of a magnet to attract or repel other magnetic substance encircled in its magnetic field or magnetic circumzone.Electromagnetism is the process of inducing E.M.F (ElectroMotive Force) in a material due to change in magnetic flux caused due to change in current across a magnet.\(.\)
Answer:
Answer of Magnetism
;- the ability to attract and charm people
OR
Magnetism is the force exerted by magnets when they attract or repel each other. Magnetism is caused by the motion of electric charges. Every substance is made up of tiny units called atoms. ... Their movement generates an electric current and causes each electron to act like a microscopic magnet
Answer of electromegnetism
Electromagnetism is defined as an attraction between particles which is defined as created by electricity. An example of electromagnetism is the force which is the basic operation of an electric motor. ... The branch of physics that deals with the interaction of electric and magnetic fields.
Explanation:
What is Moral subjectivism?
Answer:
What Is Moral Subjectivism? Moral subjectivism is based on an individual person's perspective of what is right or wrong. An individual can decide for themselves that they approve or disapprove of a certain behavior, and that is what determines if the behavior is right or wrong.
Part
An object with a charge of 3.53 pc experiences a force of 0.0147 N when it moves at right angles to a magnetic field traveling at 2342 m/s. Find the strength of the
magnetic field
Answer:
4.05 000 the about id
Explanation:
Activities 1. Find the force needed to accelerate a mass of 40kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10s
The force needed to accelerate a mass of 40 kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10 seconds is 12.4 N.
Start by calculating the change in velocity (Δv) experienced by the object. This can be done by subtracting the initial velocity v₁ from the final velocity v.
Δv = v - v₁ = ((8î + 3) - 5k) - ((4î - 5) + 3k)
= 8î + 3 - 5k - 4î + 5 - 3k
= 4î - 8k + 8
Next, calculate the acceleration (a) using the formula:
a = Δv / t
where t is the time interval, given as 10 seconds.
a = (4î - 8k + 8) / 10
= (0.4î - 0.8k + 0.8) m/s²
The force (F) required to accelerate the object can be found using Newton's second law:
F = m * a
where m is the mass, given as 40 kg.
F = (40 kg) * (0.4î - 0.8k + 0.8) m/s²
= (16î - 32k + 32) N
Simplify the expression to obtain the final answer:
F = 16î - 32k + 32 N
≈ 12.4 N
Therefore, the force needed to accelerate a mass of 40 kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10 seconds is approximately 12.4 N.
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two people are standing on the edge of a building that is 42 meters high. One person throws a tennis ball straight downward at a speed of 16 m/s. At the same exact time the other person throws a tennis ball straight upward at a speed of 16m/s. How long after the first tennis ball lands will the second tennis ball arrive at the ground?
Answer:
The second tennis ball will arrive at the ground 3.26 seconds after the first tennis ball lands.
Explanation:
Let's start by finding the time it takes for the first tennis ball to reach the ground. We can use the formula:
h = 1/2 gt^2 + v0t + h0
where:
h = height (in this case, 42 meters, since the ball is thrown from the top of the building)
g = acceleration due to gravity (9.8 m/s^2)
v0 = initial velocity (in this case, -16 m/s, since the ball is thrown downward)
h0 = initial height (in this case, 0 meters)
We want to solve for t, the time it takes for the first ball to hit the ground. We can rearrange the equation to solve for t:
t = sqrt(2h/g)
t = sqrt(2 x 42/9.8) = 3.23 seconds (rounded to two decimal places)
So the first tennis ball takes 3.23 seconds to hit the ground. Now we can use this time to find out when the second tennis ball will arrive at the ground.
The second tennis ball is thrown upward with an initial velocity of 16 m/s, and we know that it will eventually hit the ground with a final velocity of -16 m/s (the same speed as the first ball). We can use the formula:
v = v0 + gt
to find out how long it takes for the second ball to reach a velocity of 0 m/s (when it reaches the highest point of its trajectory) and then use this time to calculate the total time it takes for the ball to hit the ground.
At the highest point of its trajectory, the second ball has a velocity of 0 m/s. We can use the formula to solve for the time it takes to reach this point:
0 = 16 - 9.8t
t = 16/9.8 = 1.63 seconds (rounded to two decimal places)
It takes 1.63 seconds for the second ball to reach the highest point of its trajectory. From this point, it will take the same amount of time to reach the ground as it took for it to reach the highest point, so the total time it takes for the second ball to hit the ground is:
t = 1.63 + 1.63 = 3.26 seconds (rounded to two decimal places)
A 10.5 kg board 6.00 m long is
supported by two sawhorses, one at each end. A 4.45 kg saw sits on the board 1.80 m from the left end. Find the upward force that the LEFT sawhorse exerts on the board.
Answer: Omitting g for weigh because problem omits g
Taking torque about left sawhorse
Mr * 6 = 3 * 10.5 + 4.45 * 1.8 = 31.5 + 8.0 = 39.5
Mr = 39.5 / 6 = 6.60 mass exerted upward by right sawhorse
6.6 + Ml = 10.5 + 4.45 balancing upward and downward mass
Ml = 8.4 kg upward force (kg) exerted by left sawhorse
Check: take torque about right end
8.4 * 6 = 3 * 10.5 + 4.45 * 4.2
50.4 = 31.5 + 18.7 = 50.2 balances within rounding error
The upward force that the left sawhorse exerts on the board is 164 N.
What is meant by torque ?Torque is defined as the rotational analogue of force. It is the cross product of force and the perpendicular distance.
Here,
Mass of the board, m₁ = 10.5 kg
Length of the board, L = 6 m
Torque of the board, τ₁ = m₁g x r₁
τ₁ = 10.5 x 9.8 x (6/2)
τ₁ = 308.7 Nm
Mass of the saw, m₂ = 4.45 kg
Length of the saw, r₂ = 6 - 1.8 = 4.2 m
Torque of the saw, τ₂ = m₂g x r₂
τ₂ = 4.45 x 9.8 x 4.2
τ₂ = 183.2 Nm
So,
Torque on the left saw = Torque on the board + torque on the saw
τ' = 308.7 + 183.2
τ' = 491.9
Therefore force exerted by the left saw, F = τ'/(L/2) = 491.9/3
F = 164 N
Hence,
The upward force that the left sawhorse exerts on the board is 164 N.
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