Work done by the normal force is about 78.4 N, and work done by the gravitational force is about 135.8 J. Option D.
Calculation:
M = 8kg
O =60
work done by the gravity
Wa= \(\int\limits^_ {} \,\) FG. ds = \(\int\limits^_ {} \,\)FG. ds cos (90-60)
Wa = \(\int\limits^2_0 {} \,\) mg cos30. ds
Wa = \(\int\limits^2_0 {} \,\)8x9.8x0.866.ds
Wa = 135.788 N.m ≈ 135.8 J
Work done by the normal force
WN= \(\int\limits^_ {} \,\)N.ds = \(\int\limits^_ {} \,\)N.ds cos90°.
The normal force is the force exerted by a surface to prevent solid objects from passing through each other. The normal force is the contact force. If two surfaces are not in contact, they cannot exert a force perpendicular to each other. The normal force is defined as the force that a surface exerts on another body. When this object is at rest it means that the net force acting on the object is zero.
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QUIZ
Matter
Three materials, labeled A, B, and C, are being
considered for a new product. An important criterion,
or goal for the product, is the ability to float in water.
This data table shows the mass, volume, and density
of samples of the three materials and a sample of
matter.
Which material best meets the criterion?
Select the correct word from each drop-down menu
to complete the answer.
The best choice is material A
material has a density ✓that is
loss
than that of water.
Only this
Material Mass Volume
100 g
100 cm³
water
A
B
C
12
100 g
100 g
40 g
500 cm³
50 cm³
10 cm³
Density
1.0 g/cm³
0.20 g/cm³
2.0 g/cm³
4.0 g/cm³
Rood
This is science btw
The only object that could be able to float in water is the object A because it has a density that is less than that of water.
What is density?The term density has to do with the ratio of the mass to the volume of an object. We know that the volume is one of the properties of the material that we call the intrinsic properties. These are the properties that could be used in the identification of the material because they do not change.
The density of water is obtained as 1.00g/mL. The object that would float in water must have a density that is less than that of water. The only object that could be able to float in water is the object A because it has a density that is less than that of water.
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Two projectiles are thrown with the same initial velocity, one at an angle and the other at an angle of . (a) Can both projectiles strike the ground at the same distance from the projection point? (b) Can both projectiles be in air for the same time interval?
Answer:
si quiero ser tu novia❤❤
In medieval warfare, one of the greatest technological advancement was the trebuchet. The trebuchet was used to sling rocks into castles. You are asked to study the motion of such a projectile for a group of local enthusiast planning a medieval war reenactment. Unfortunately an actual trebuchet had not been built yet, so you decide to first look at the motion of a thrown ball as a model of rocks thrown by a trebuchet. Specifically, you are interested in how the horizontal and the vertical components of the velocity for a thrown object change with time. 1. Make a large rough sketch of the trajectory of the ball after it has been thrown. Draw the ball in at least five different positions; two when the ball is going up, two when it is going down, and one at its maximum height. Label the horizontal and vertical axes of your coordinate system.
2. On the sketch, draw and label the expected acceleration vectors of the ball (relative sizes and directions) for the five different positions. Decompose each acceleration vector into its vertical and horizontal components.
3. On the sketch, draw and label the velocity vectors of the object at the same positions you chose to draw your acceleration vectors. Decomposes each velocity vector into its vertical and horizontal components. Check to see that the changes in the velocity vector are consistent with the acceleration vectors.
4. Looking at the sketch, how does someone expect the ball's horizontal acceleration to change with time? Could you give a possible equation giving the ball's horizontal acceleration as a function of time? Graph this equation. If there are constants in your equation, what kinematic quantities do they represent? How would someone determine these constants from the graph?
5. Looking at the sketch, how does someone expect the ball's horizontal velocity to change with time? Is it consistent with the statements about the ball's acceleration from the previous question? Could you give a possible equation for the ball's horizontal velocity as a function of time? Graph this equation. If there are constants in the equation, what kinematic quantities do they represent? How would someone determine these constants from the graph?
6. Could you give a possible equation for the ball's horizontal position as a function of time? Graph this equation. If there are constants in the equation, what kinematic quantities do they represent? How would someone determine these constants from the graph? Are any of these constants related to the equations for horizontal velocity or acceleration?
7. Repeat questions 4-6 for the vertical component of the acceleration, velocity, and position. How are the constants for the acceleration, velocity and position equations related?
Answer:
2) a_y= -g 3) vₓ=constant v_y = v_{oy} - g t, 4) vₓ = v₀ₓ - ax t
5) changes the horizontal speed, should change range
7) changes the vertical speed change the maximum height
Explanation:
1) After reading your long writing, we are going to solve the exercise, in the attachment you can see the different vectors.
2) The acceleration vectors are vertical and directed downwards due to the attraction of the Earth (gravity force) this force is constant, on the x axis there is no acceleration
3) the velocity vectors on the x-axis are constant because there are no relationships and the y-axis changes value according to the expression
v_y = v_{oy} - gt
at the point of maximum height, vy = 0 is equal to the maximum height
4) For someone to change the horizontal acceleration we must assume a friction with the air, in this case they relate it would be in the opposite direction to the horizontal speed
In the graph it would be directed to the left, therefore the velocity would be
vₓ = v₀ₓ - ax t
5 and 6) If someone changes the horizontal speed, they should change the range of the shot for greater horizontal speed, the rock goes further.
the equations of motion are
x = v₀ₓ t
y = v_{oy} t - ½ g t²
7) If someone changes the vertical speed change the maximum height, but not the scope of the shot, for higher speed higher maximum height,
the equations of motion are the same.
An object has mass 4 kg. What is its weight (in newton) on earth?
Answer:
Should be -39.2 N
Explanation:
w=mg
w=4 x -9.8 m/s2
= -39.2 N
The resistance in question is known to have an approximate value of 500 Ω. This resistance is placed in a Wheatstone bridge with three other arms having exactly 500 Ω resistances. A 3.7 V battery with negligible internal resistance is used in the circuit. The galvanometer has a resistance of 80 Ω and a current of 0.08 μA. Calculate the value of the unknown resistance.
The value of the unknown resistance is approximately 44750 Ω.
In a balanced Wheatstone bridge, the ratio of the resistances in the two arms of the bridge is equal to the ratio of the resistances in the other two arms. That is:
R1/R2 = R3/R4
where R1, R2, R3, and R4 are the resistances in the four arms of the bridge.
In this problem, the resistances in three of the arms of the bridge are all exactly 500 Ω. Let the resistance in the fourth arm (the unknown resistance) be denoted by R. The voltage across the galvanometer is zero in a balanced Wheatstone bridge, so the current through the galvanometer is also zero.
Using Ohm's law, the current through the entire circuit is given by:
I = V/(R1 + R2 + R3 + R4)
where V is the voltage of the battery, and R1, R2, R3, and R4 are the resistances in the four arms of the bridge.
The voltage drop across the 500 Ω resistances is given by:
V_500 = (500/(500+500+R)) * V
The voltage drop across the unknown resistance R is also given by:
V_R = (R/(500+500+R)) * V
Since the voltage across the galvanometer is zero, the current through the unknown resistance R is equal to the current through the 80 Ω galvanometer. Using Ohm's law, we can write:
I_R = V_R/R = I_galvanometer = 0.08 μA
Substituting the expressions for the voltages and the current into the equation for the total current, we get:
V/(500+500+500+R) = 0.08 μA
Solving for R, we get:
R = (V/0.08 μA) - 1500 Ω
Substituting the given values, we get:
R = (3.7 V)/(0.08 μA) - 1500 Ω
R = 46250 Ω - 1500 Ω
R = 44750 Ω
Therefore, the value of the unknown resistance is approximately 44750 Ω.
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Which kind of bond forms ions?
Answer:
Ionic bond
Explanation:
Hope it helps ya
a. When throwing a ball vertically upward, my hand moves through a distance of about 1.0 m before the ball leaves my hand. The 0.80 kg ball reaches a maximum height of about 20 m above my hand. while the ball is in my hand after the ball leaves my hand
The required, it experiences a downward force due to gravity and a force due to air resistance.
What is the projectile motion?Projectile motion is the movement of an entity projected into space. After the initial force that launches the object, it only experiences the force of gravity. The object is called a projectile, and its path is called its trajectory.
Here,
When throwing a ball vertically upward, there is a displacement of about 1.0 m from the initial position of the hand to the position where the ball leaves the hand. The mass of the ball is 0.80 kg and it reaches a maximum height of about 20 m above the initial position of the hand. While the ball is in the hand after it leaves, it experiences a downward force due to gravity and a force due to air resistance.
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An atom undergoes nuclear decay, but its atomic number is not changed.
What type of nuclear decay did the atom undergo?
A. Gamma decay
B. Beta decay
C. Nuclear fission
D. Alpha decay
Answer:
A. Gamma decay
Explanation:
A form of nuclear decay in which the atomic number is unchanged is a gamma decay.
The atom has undergone a gamma decay.
In a gamma decay, no changes occur to the mass and atomic number of the substance.
Gamma rays have zero atomic and mass numbers. When they cause decay, they cause no change to the mass and atomic numbers. They simply produce gamma rays during such reactions and these rays are very energetic.Can you give me the answers with being very organized Ans just explain goood
Explanation
the equation is base ond the Pythagorean theorem,it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
\(a^2+b^2=c^2\)so,
Step 1
if
\(undefined\)A car traveled 190 km in 2.5 hours what was its average speed in km per hour
We have the next information
d=190km
t=2.5 hour
Because the speed is requested in km per hour we don't need to change any unit so we only use the next formula
\(v=\frac{d}{t}\)\(v=\frac{190}{2.5}=76\text{ km per hour}\)Help please :)
Ultraviolet waves are transmitted by ....... ?
Answer:
Sunlight is the greatest source of UV radiation. Man-made ultraviolet sources include several types of UV lamps, arc welding, and mercury vapour lamps.
Explanation:
A bird lands on a bird feeder which is connected to a spring. The mass of the bird is exactly the same as the mass of the bird feeder. How does the added mass affect the period of oscillation of the bird feeder?
Answer:
The added mass will mean a longer period of oscillation.
Explanation:
The period of oscillation here is given by the formula;
T = 2π√(m/k)
Where m is mass and k is spring constant
From the equation of oscillation period above, it's obvious that when we increase the mass, the oscillation period will also increase.
Thus, the added mass will mean a longer period of oscillation.
The diagram below shows three kettles with their powers and the time they take to boil 500cm3 of water. If electricity costs 9p per unit, how much does it cost to boil 500cm3 of water using the 1.4kW kettle?
NOTE IF YOU ARE RIGHT YOU WILL GET A BRAINLY!!
The cost of boiling 500 cm³ of water using 1.4kW kettle is 0.945 p
How do I determine the cost of boiling water using 1.4 KW kettle?We shall begin our calculation by obtaining the energy consumed when using 1.4 KW kettle. This is shown below:
Power (P) = 1.4 KW Time (t) = 4.5 minutes = 4.5 / 60 = 0.075 hoursEnergy (E) =?E = Pt
E = 1.4 × 0.075
E = 0.105 KWh
Finally, we shall determine the cost of boiling the water using the 1.4 KW kettle. Details below
Cost per KWh = 9 pEnergy (E) = 0.105 KWhCost of boiling =?Cost = energy × Cost per KWh
Cost of boiling = 0.105 × 9
Cost of boiling = 0.945 p
Thus, we can conclude that the cost of boiling is 0.945 p
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A person is dragging a crate over a shag carpet with a push force of 10N. The shag rug creates a friction force of 5N. The mass of the crate is 5 k
g. Calculate the acceleration of the crate?
(Just enter the numbers, no
The acceleration of the crate after the frictional force is overcame is determined as 1 m/s².
What is acceleration?Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity with time.
The acceleration of the crate is calculated from the net force acting on the crate as shown below;
F(net) = applied force - frictional force
F(net) = 10 N - 5N
F(net) = 5 N
Apply Newton's second law of motion to calculate the acceleration of the crate.
F(net) = ma
where;
m is mass of the cratea is acceleration of the cratea = F(net) / m
a = 5/5
a = 1 m/s²
Thus, the acceleration of the crate after the frictional force is overcame is determined as 1 m/s².
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19. Assume this process is 10% efficient, how much work is done by the gas expanding into the atmosphere?
The amount of work done by the gas is proportional to the pressure and the change in volume, as well as the efficiency of the process. If the pressure and volume are known, the work done by the gas can be calculated by multiplying these values by the efficiency of the process.
The amount of work done by a gas when it expands is proportional to the change in volume, pressure, and temperature. According to the first law of thermodynamics, the energy of a closed system is conserved, so the work done by the expanding gas is equal to the energy transferred from the gas to the environment in the form of work. Therefore, the work done by the gas is equal to the change in energy of the system. Assume that the process is 10% efficient. Then, only 10% of the energy available to the system is converted into work. This means that the remaining 90% of the energy is lost to the environment in the form of heat. As a result, the amount of work done by the gas expanding into the atmosphere is given by the formula
W = E x η, where W is the work done by the gas, E is the energy available to the system, and η is the efficiency of the process. The energy available to the system is determined by the difference between the internal energy of the gas before and after the expansion. The internal energy of a gas is determined by its temperature, pressure, and volume.
Assuming that the temperature and pressure are constant, the change in internal energy is proportional to the change in volume. Therefore, the energy available to the system is equal to the product of the pressure and the change in volume: E = P x ΔV, where P is the pressure of the gas and ΔV is the change in volume during the expansion. Substituting this equation into the formula for work, we get W = P x ΔV x η.
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A spring-loaded ballistic cart measuring 0.68 kg is in contact with a second 0.80 kg
cart. The carts are initially at rest on a level surface. The spring is released and the
lighter cart is observed to move at +0.52 m/s afterward. What is the velocity of the
other cart?
Answer:
wait in comments.................
As part of astronaut training, a prospective astronaut is spun around in a human centrifuge such that the candidate experiences a centripetal acceleration that is 2.8 times the acceleration due to gravity on the surface of the earth. If the candidate is 11.05 m from the center, determine the candidate's speed in meters per second.
The candidate's speed (m/s), given that the candidate experiences a centripetal acceleration that is 2.8 times the acceleration due to gravity is 17.4 m/s
How do I determine the candidate's speed?We understood that the centripetal acceleration is related to speed and radius according to the following formula:
a = v² / r
Cross multiply
v² = ar
Take the square root of both sides
v = √ar
Where
v is the speeda is the centripetal accelerationr is the radiusWithe the above formula, we can determin the speed of the candidate. Details below:
Acceleration due to gravity (g) = 9.8 m/s²Centripetal acceleration = 2.8 × g = 2.8 × 9.8 = 27.44 m/s²Radius (r) = 11.05 mSpeed of candidate (v) =?v = √ar
v = √(27.44 × 11.05)
v = 17.4 m/s
Thus, the speed of the candidate is 17.4 m/s
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What is an indicator?
A. An organic compound that changes color in acids and bases
B. A strong acid
C. The amount of ions in solution
D. The concentration of acids or bases
What do you still wonder about force and motion as it relates to the pod and asteroid collection mission that did not go as planned?.
To collect the asteroid an equal magnitude of the force in opposite direction is needed.
What is force ?
The motion or speed of an object depends upon the magnitude and the direction of the force.
If the direction of the force is against the direction of motion, then the object will slow down or stop. The two forces of the same magnitude in the opposite direction cancel each other and the collided objects stop each other.
Therefore, to collect the asteroid an equal magnitude of the force in opposite direction is needed.
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what is the velocity of the object 2.3 seconds after it is released from the top of the empire state building?
Explanation:
Object is under the effect of the acceleration of gravity
v = 1/2 a t^2 a = 9.81 m/s^2 t = 2.3
v = 25.9 m/s^2 = ~ 26 m/s ( two significant digits)
Three masses lie on the x-axis. Object A is at the origin and has a mass of 199.1 kg. Object B has a mass of 592.9 kg and is located 7.5 meters in the positive x direction from A. Finally, object C, which has a mass of 330 kg, is positioned 4 meters from object B, so that object B is between objects A and C. What is the force acting on object A? (The sign of your answer will denote direction.)
The force on A is _____?
The net force on A is 1.7312 × 10⁻⁷ N
Newton's law of universal gravitation
It states that the force of attraction between two masses M and m is directly proportional to the product of their masses and inversely proportional to the square of their distance apart, R.
So, F = GMm/R² where G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg²
Force of attraction between A and BNow let
m₁ = mass of object at A = 199.1 kg, m₂ = mass of object at B = 592.9 kg and R = distance between object at A and B = 7.5 m.So, the force of attraction between them is
F = Gm₁m₂/R₁² (positive since it is directed towards B in the positive x direction)
Substituting the values of the variables into the equation, we have
F = Gm₁m₂/R₁²
F = 6.67 × 10⁻¹¹ Nm²/kg² × 199.1 kg × 592.9 kg/(7.5 m)²
F = 787369.4213 × 10⁻¹¹ Nm²/56.25 m²
F = 13997.68 × 10⁻¹¹ N
F = 1.399768 × 10⁻⁷ N
F ≅ 1.3998 × 10⁻⁷ N
Force of attraction between A and C
Also, let
m₁ = mass of object at A = 199.1 kg, m₃ = mass of object at C = 330 kg,and R₂ = distance between object at A and C = 4 m + 7.5 m = 11.5 mSo, the force of attraction between them is
F' = Gm₁m₃/R₂² (positive since it is directed towards C in the positive x direction)
Substituting the values of the variables into the equation, we have
F' = Gm₁m₂/R₁²
F' = 6.67 × 10⁻¹¹ Nm²/kg² × 199.1 kg × 330 kg/(11.5 m)²
F' = 438239.01 × 10⁻¹¹ Nm²/132.25 m²
F' = 3313.72 × 10⁻¹¹ N
F' = 0.331372 × 10⁻⁷ N
F' ≅ 0.3314 × 10⁻⁷ N
Net force on A
So, the net force acting on object A is F" = F + F'
= 1.3998 × 10⁻⁷ N + 0.3314 × 10⁻⁷ N
= 1.7312 × 10⁻⁷ N
So, the net force on A is 1.7312 × 10⁻⁷ N
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Mrs Turner has a scale drawing of her apartment.IN the scale drawing the lenght of her apartment is 6.25 inches and the width is 2.75 onches. If Mrs. Turner used the scale factor 1 inc/18ft, what would the area of the apartment be?
The area of Mrs. Turner's apartment is approximately 0.05304 square feet.
To find the area of Mrs. Turner's apartment, we need to convert the measurements from the scale drawing to the actual measurements in feet, using the given scale factor of 1 inch/18 feet.
Length of apartment in feet = 6.25 inches × (1 foot/18 inches) = 0.34722 feet
Width of apartment in feet = 2.75 inches × (1 foot/18 inches) = 0.15278 feet
Now, we can calculate the area of the apartment in square feet by multiplying the length and width:
Area of apartment in square feet = Length × Width = 0.34722 feet × 0.15278 feet = 0.05304 square feet
Therefore, the area of Mrs. Turner's apartment is approximately 0.05304 square feet.
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Joe is painting the floor of his basement using a paint roller. The roller has a mass of 2.4 kg and a radius of 3.8 cm. In rolling the roller across the floor, Joe applies a force F = 16 N directed at an angle of 35° as shown. Ignoring the mass of the roller handle, what is the magnitude of the angular acceleration of the roller?
The magnitude of the angular acceleration of the roller is approximately 108.8 rad/s².
To find the magnitude of the angular acceleration of the roller, we can use the rotational analog of Newton's second law: τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
First, let's calculate the moment of inertia of the roller. The moment of inertia of a solid cylinder rotating about its central axis is given by the formula: I = (1/2)mr², where m is the mass and r is the radius.
Given:
Mass of the roller (m) = 2.4 kg
Radius of the roller (r) = 3.8 cm = 0.038 m
Moment of inertia (I) = (1/2) * 2.4 kg * (0.038 m)² = 0.0021744 kg·m²
Next, we need to calculate the torque (τ) applied to the roller. Torque is given by the formula: τ = rFsin(θ), where r is the distance from the axis of rotation to the point of application of the force, F is the magnitude of the force, and θ is the angle between the force and the line connecting the axis of rotation and the point of application.
Given:
Force applied (F) = 16 N
Angle (θ) = 35°
Distance from the axis of rotation to the point of application (r) is equal to the radius of the roller, so r = 0.038 m.
Torque (τ) = (0.038 m) * (16 N) * sin(35°) = 0.2366 N·m
Now, we can use the equation τ = Iα and solve for the angular acceleration (α):
0.2366 N·m = (0.0021744 kg·m²) * α
α = 0.2366 N·m / 0.0021744 kg·m² ≈ 108.8 rad/s²
Therefore, the magnitude of the angular acceleration of the roller is approximately 108.8 rad/s².
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A 2.8 kg block slides along a frictionless surface at 1.1 m/s . A second block, sliding at a faster 4.8 m/s , collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.3 m/s.
What was the mass of the second block?
Conservation of momentum is a major law of physics which states that the momentum of a system is constant if no external forces are acting on the system. It is embodied in Newton’s First Law or The Law of Inertia.the mass of the second block is 1.1Kg.
principle of momentum conservation
M1u1 plus M2u2 equals M1v1 and M2V2.
As all collisions were elastic in nature and no energy loss through friction, heat, etc. was taken into account, theoretic calculations alone cannot guarantee that there was a complete transfer of energy.
Consider the scenario where a football with mass M2 is lying on the ground and a bowling ball with mass M1 is hurled at the football at a velocity of
The formula is: (2.8 kg * 1.1 m/s) + (m2 * 4.8 m/s) = (2.3 kg + m2). 2.3 m/s
The formula is 2.8 J + (4.8 m/s m2) = 4.8 J + (2.3 m/s m2).
4.8 m/s m2 = 2.8 J plus (2.3 m/s m2)
4.8 m2 = 2.8 + 2.3 m2
2.3 m2 on each side of the equation
2.5 m = 2.8 m = 2.8 / 2.5\sm = 1.1kg
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A fullback moving south has a collision with an opponent running north. What type of collision is
it? Explain.
When a fullback moving south has a collision with an opponent running north, it is a type of head-on collision.
What are the types of collision?
1. Elastic collision: A collision in which the total kinetic energy of the system remains the same, and kinetic energy is exchanged between objects.
2. Inelastic collision: A collision in which the total kinetic energy of the system is not conserved, and some kinetic energy is converted into other forms, such as heat or sound.
3. Perfectly inelastic collision: A collision in which the total kinetic energy of the system is completely converted into other forms, such as heat or sound.
4. Partially inelastic collision: A collision in which the total kinetic energy of the system is partially conserved, and some kinetic energy is converted into other forms, such as heat or sound.
5. Plastic collisions: A collision in which the kinetic energy of the system is partially conserved, but some energy is also converted into permanent deformation.
The collision you described between the fullback moving south and the opponent running north is an example of a head-on collision. A head-on collision is defined as a type of collision where two objects collide with each other while moving in opposite directions. These types of collisions are often considered the most dangerous, due to the high energy that is released as the two objects collide.
Therefore, head-on collision is the answer.
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QUESTION 1
The two human thighbones (femurs) each have a cross-sectional area of 10 cm and they support
the upper part of a human body of mass 40kg. Calculate the average pressure sustained by each of
the femurs. (1mk)
Answer:
2 * 10^5 pa
Explanation:
Pressure = Force / Area
Each thigh bone has a cross sectional area of 10cm²
Both thigh bones :
2 * 10cm² = 20cm²
To m² : 20 * (0.01)²
20 * 0.0001 m² = 0.002 m²
Force = mass * acceleration due to gravity(g)
g = 10m/s² ;
Force = 40 * 10 = 400N
Pressure = 400 N / 0.002 m²
Pressure = 200,000 N/m² = 2 * 10^5 pascal
The road runner was being chased and outsmart the coyote. He ran past the road runner an fell straight down off a cliff. He fell with the same acceleration as gravity (9.8). Calculate his displacement if he fell for 4 seconds
The displacement of the runner after four seconds is 78.4 m.
What is the displacement after 4 seconds?We know that in this case, we are dealing with a case of an object that has a motion under gravity. We are told that the road runner an fell straight down off a cliff. The fact that we have been told that the runner just fell down the cliff means that the initial velocity of the runner would have to be taken in this context as zero since the runner was dropped from a height as shown.
Acceleration of the runner (g) = 9.8 m/s^2
Initial velocity of the runner (u) = 0 m/s
Time take (t) = 4 seconds
We then have;
h = ut + 1/2gt^2
If we then know that the initial velocity of the person is zero, then we have;
h = 1/2gt^2
h = 0.5 * 9.8 * (4)^2
h = 78.4 m
The height is 78.4 m.
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A 10 kg piano is hoisted on a crane and delivered through the window of a six story apartment 20 m above the ground what is the potential energy of the piano?
Answer:
1962 J
Explanation:
potential energy= mgh
m=10 kg
h=20 m
g=9.81 (always unless otherwise stated)
PE= 10(20)(9.81)=1962 J
Find the surface of each pyramid round to nearest tenth if necessary
12.2m
16m
10.6m
12.2m
12.2m
Surface area of pyramid 1 539.2 \(m^{2}\) Pyramid 2: 370.9 \(m^{2}\) Pyramid 3: 446.4 \(m^{2}\)
To find the surface area of a pyramid, we need to know the dimensions of its base and its slant height. Assuming the base of each pyramid is a square, we can calculate the surface area using the formula:
Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height)
Let's calculate the surface area for each pyramid using the given dimensions:
1. Pyramid 1: Base = 12.2 m Slant Height = 16 m Base Area = (12.2 \(m^2\)= 148.84 \(m^2\)Perimeter of Base = 4 × 12.2 m = 48.8 m
Surface Area = 148.84 \(m^2\)+ (0.5 × 48.8 m × 16 m) = 148.84 m^2 + 390.4 \(m^2\) = 539.24 \(m^2\) (rounded to nearest tenth)
2. Pyramid 2: Base = 10.6 m Slant Height = 12.2 m Base Area = (10.6 \(m^2\))= 112.36\(m^2\) Perimeter of Base = 4 × 10.6 m = 42.4 m
Surface Area = 112.36\(m^2\)+ (0.5 × 42.4 m × 12.2 m) = 112.36 \(m^2\)+ 258.56 \(m^2\) = 370.92 \(m^2\)(rounded to nearest tenth)
3. Pyramid 3: Base = 12.2 m Slant Height = 12.2 m Base Area = (12.2 \(m^2\)= 148.84 \(m^2\)Perimeter of Base = 4 × 12.2 m = 48.8 m
Surface Area = 148.84 m^2 + (0.5 × 48.8 m × 12.2 m) = 148.84 \(m^2\)+ 297.52 \(m^2\) = 446.36 \(m^2\) (rounded to nearest tenth)
Therefore, the surface areas of the given pyramids are approximately: Pyramid 1: 539.2 \(m^2\)Pyramid 2: 370.9 \(m^2\) Pyramid 3: 446.4 \(m^2\).
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What is the acceleration of a box weighing 596 N if a force of 777 N is applied to it?
Answer:
\(12.79 m/s^2\)
Explanation:
1. Apply Newton's 2nd law:
\(F=ma\)
2. Use the definition of weight to find the mass of the box:
\(W=mg=m=\frac{W}{g}\)
3. Solve for acceleration in Newton's 2nd law and substitute for mass:
\(a=\frac{F}{\frac{W}{g} }\)
4. Plug in the given values from the question and assume \(g=9.81m/s^2\):
\(a=\frac{777N}{\frac{596N}{9.81m/s^2} } } =12.79m/s^2\)