1. You slowly lift a book of mass 2 kg at a constant velocity a distance of 3 m. How much work did you do on the book?
I got 180 for this
2. A 15 kg crate is moved along a horizontal floor with a rope that makes a 30 degree angle with the horizontal. If the tension in the rope is 200 N and the crate is slid 10 meters, how much work has been done on the crate?
3. True or False: An object that is motionless has no energy
4. What is the kinetic energy of a ball of mass .1 kg traveling at a speed of 160 m/s?
5. Assuming air resistance is zero (negligible), how high up would a .06 kg tennis ball travel if hit straight into the air at initial speed of 50 m/s?
6. A stunt woman scales a 40 meter high cliff. What is her potential energy due to gravity relative to the ground?
7. Imagine you are 100 kg and standing at the edge of a hole that goes to the center of the earth. What is your potential energy relative to the center of the earth?
1. The work done is W = M g H
H is the distance it is lifted
Try again
You need to review the definitions of potential and kinetic energy and make an effort on the other questions.
1. To calculate the work done on the book, you can use the formula:
Work = Force x Distance x cos(theta)
where Force is the weight of the book (mass x gravity), Distance is the distance you lifted the book, and theta is the angle between the force applied and the direction of motion (which is 0 degrees since the book is lifted vertically).
In this case, the work done on the book is given by:
Work = (2 kg x 9.8 m/s^2) x 3 m x cos(0 degrees)
Work = 19.6 N x 3 m x 1
Work = 58.8 Joules
Therefore, the work done on the book is 58.8 Joules, not 180.
2. To calculate the work done on the crate, you can use the same formula as in question 1:
Work = Force x Distance x cos(theta)
In this case, the force applied is the tension in the rope (200 N), the distance is 10 meters, and the angle theta is 30 degrees.
Work = 200 N x 10 m x cos(30 degrees)
Work = 200 N x 10 m x (√3/2)
Work = 1000 (√3/2) Joules
Therefore, the work done on the crate is approximately 1732 Joules.
3. False. An object that is motionless still has potential energy. Potential energy is the energy an object possesses due to its position. Even if an object is not moving, it can have potential energy, such as gravitational potential energy or elastic potential energy.
4. To calculate the kinetic energy, you can use the formula:
Kinetic Energy = (1/2) x mass x velocity^2
In this case, the mass of the ball is 0.1 kg and the velocity is 160 m/s.
Kinetic Energy = (1/2) x 0.1 kg x (160 m/s)^2
Kinetic Energy = 0.8 x 160^2
Kinetic Energy = 0.8 x 25600
Kinetic Energy = 20480 Joules
Therefore, the kinetic energy of the ball is 20480 Joules.
5. To calculate the maximum height reached by the tennis ball, you can use the conservation of mechanical energy. The initial mechanical energy (kinetic energy) is converted into potential energy at the highest point.
The initial mechanical energy is given by:
Mechanical Energy = (1/2) x mass x velocity^2
In this case, the mass of the tennis ball is 0.06 kg and the velocity is 50 m/s.
Mechanical Energy = (1/2) x 0.06 kg x (50 m/s)^2
Mechanical Energy = 0.03 x 2500
Mechanical Energy = 75 Joules
At the maximum height, all the kinetic energy is converted into potential energy:
Potential Energy = mass x gravity x height
In this case, the mass is 0.06 kg, gravity is 9.8 m/s^2, and we need to find the height.
75 Joules = 0.06 kg x 9.8 m/s^2 x height
height = 75 Joules / (0.06 kg x 9.8 m/s^2)
height ≈ 126.26 meters
Therefore, the tennis ball would reach a height of approximately 126.26 meters.
6. The potential energy due to gravity is given by the formula:
Potential Energy = mass x gravity x height
In this case, the mass is not specified, so we'll assume it's the mass of the stunt woman. The height is 40 meters and the value of gravity is 9.8 m/s^2.
Potential Energy = 40 m x 9.8 m/s^2 x mass
The potential energy is relative to the ground, so it is independent of the mass. Therefore, we can say that the potential energy is simply:
Potential Energy = 40 m x 9.8 m/s^2
Potential Energy = 392 Joules
Therefore, the potential energy of the stunt woman due to gravity is 392 Joules.
7. The potential energy relative to the center of the earth can be calculated using the formula:
Potential Energy = mass x gravity x height
In this case, the mass is 100 kg, the height to the center of the earth is the radius of the earth (approximately 6,371 kilometers or 6,371,000 meters), and the value of gravity is 9.8 m/s^2.
Potential Energy = 100 kg x 9.8 m/s^2 x 6,371,000 m
Potential Energy = 6,223,180,000 Joules
Therefore, your potential energy relative to the center of the earth is approximately 6,223,180,000 Joules.