PE & KE Quiz 2

Explanation
The gravitational potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. Comparing the given options, the object with the greatest gravitational potential energy would be the one with the highest product of mass and height. Therefore, the 20-kg mass at 50-m height would have the greatest gravitational potential energy.

Explanation
When the glider dives to a lower altitude, its potential energy decreases. The change in potential energy can be calculated using the formula ΔPE = mgh, where m is the mass of the glider, g is the acceleration due to gravity, and h is the change in altitude. Plugging in the given values, ΔPE = (12.5 kg)(9.8 m/s^2)(1,510 m - 1,250 m) = 31,900 J. Therefore, the change in potential energy of the glider is 31,900 J.

Explanation
The kinetic energy of an object is directly proportional to its mass and the square of its velocity. Since the father and the son are jogging at the same speed, their velocities are equal. However, the father's mass is twice that of the son. Therefore, the kinetic energy of the father is twice that of the son.

Explanation
The potential energy of an object is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, the mass of the water is 1000 kg and the average height is 50.0 m. Plugging these values into the equation, we get PE = (1000 kg)(9.8 m/s^2)(50.0 m) = 4.9 E 5 J. Therefore, the potential energy of the water in the tower is 4.9 E 5 J.

Explanation
The worker can lift the bag of sand to a height of 10.20 m because the amount of energy produced (4,000.0 J) is equal to the gravitational potential energy gained by the bag of sand when it is lifted to that height. Gravitational potential energy is given by the equation PE = mgh, where m is the mass of the object (40.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height. Rearranging the equation, h = PE/(mg), we can calculate the height to be 10.20 m.

Explanation
The height of the incline can be determined using the principle of conservation of energy. The potential energy at the top of the incline is converted into kinetic energy at the bottom of the incline. The potential energy is given by mgh, where m is the mass, g is the acceleration due to gravity, and h is the height of the incline. The kinetic energy is given by (1/2)mv^2, where v is the speed of the block at the bottom of the incline. Equating the two energies, we have mgh = (1/2)mv^2. The mass cancels out, and we can solve for h by rearranging the equation to h = (1/2)v^2/g. Plugging in the values given, we find h = (1/2)(3^2)/9.81 ≈ 0.46 m.

Explanation
Based on the given information, the skateboarder has a kinetic energy (KE) of 625 J at the bottom of the half-pipe. As the skateboarder climbs up the half-pipe, the KE is converted into potential energy (PE). The potential energy at the highest point of the half-pipe is equal to the initial kinetic energy at the bottom. Since the mass of the skateboarder is not given, we can use the conservation of energy principle. By equating the initial KE to the final PE, we can find the height the skateboarder climbs. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Solving for h, we find that the skateboarder climbs a distance of 1.3 m.

Explanation
When the rubber ball hits the wall and bounces back, its kinetic energy decreases. The kinetic energy of an object is given by the equation KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object. Since the mass of the ball remains the same, the change in kinetic energy is solely dependent on the change in velocity. The ball's velocity decreases from 4.0 m/s to 2.0 m/s, which is a decrease of half the original velocity. Therefore, the kinetic energy of the ball after bouncing off the wall is one-fourth as great as the kinetic energy before it hits the wall.

Explanation
When a spring is stretched, its elastic potential energy increases. This is because the potential energy of a spring is directly proportional to the square of its displacement. As the spring is stretched further, the displacement increases, leading to a greater potential energy. Therefore, the correct answer is increases.

Explanation
The correct answer is 1. This graph represents the relationship between gravitational potential energy and height above Earth's surface correctly. As the height increases, the gravitational potential energy also increases. This is because the potential energy is directly proportional to the height. The graph shows a positive linear relationship between the two variables.

Explanation
When the ball is dropped from the top of the building, it is initially at a certain height above the ground. As it falls, its potential energy is converted into kinetic energy. At the instant it was dropped, the ball has not yet started to move, so its kinetic energy is zero. Therefore, the total energy of the ball is equal to its potential energy. The formula for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Since the mass is given as 1.00 kg and the height is not provided, we can assume that the height is not relevant to the calculation. Therefore, the gravitational potential energy is 1.00 kg * 9.8 m/s^2 * 1 m = 9.8 J. However, the question asks for the energy relative to the ground, so we need to subtract the potential energy when the ball is at the ground level. Since the ball is dropped from the top of the building, its potential energy relative to the ground is zero at that point. Therefore, the gravitational potential energy of the ball at the instant it was dropped is 9.8 J - 0 J = 9.8 J. This is equal to 72.0 J in the given answer.