Gravitational potential energy Knowledge-Based Download PDF

Questions

1. 1.

   Strictly speaking, gravitational potential energy is stored in which of the following when an object is raised to a height above the ground?

   • A) Exclusively within the internal atomic structure of the raised object
   • B) In the external lifting agent that exerted the upward contact force
   • C) In the thermal energy of the surrounding atmospheric medium
   • D) In the gravitational field of the system consisting of the object and Earth
2. 2.

   Which of the following statements correctly relates the work done by the gravitational force, $W_g$, to the change in gravitational potential energy, $\Delta U$, for an object displaced vertically near Earth's surface?

   • A) $W_g = \Delta U$ for both upward and downward displacements.
   • B) $W_g = -\Delta U$ only when the object moves upward at constant speed.
   • C) $W_g = \Delta U$ when moving downward, but $W_g = -\Delta U$ when moving upward.
   • D) $W_g = -\Delta U$ for both upward and downward displacements.
3. 3.

   Three identical crates are moved from the ground to the same vertical height $h$ along three different paths: a direct vertical lift, a smooth inclined plane, and a stepped ramp. Which statement correctly compares the change in gravitational potential energy ($\Delta U$) of the three crates?

   • A) $\Delta U$ is greatest for the vertical lift because the lifting force acts purely in the upward direction.
   • B) $\Delta U$ is identical for all three crates because gravitational potential energy depends only on the change in vertical height.
   • C) $\Delta U$ is greatest for the inclined plane because the crate travels the greatest total distance.
   • D) $\Delta U$ is greatest for the stepped ramp because work is performed across multiple distinct stages.
4. 4.

   An object is held at a height $h$ above the ground. If its mass is increased by 20% and its height above the ground is decreased by 40%, by what percentage does its gravitational potential energy relative to the ground change?

   • A) It decreases by 20%.
   • B) It decreases by 52%.
   • C) It decreases by 48%.
   • D) It decreases by 28%.
5. 5.

   An instrument package has a gravitational potential energy of 720 J relative to the lunar surface when held at a height of 15 m above the Moon. Taking the acceleration due to gravity on the Moon to be $1.6\text{ m/s}^2$ and on Earth to be $9.8\text{ m/s}^2$, what is the gravitational potential energy of the package when held at the same height above Earth's surface?

   • A) 118 J
   • B) 294 J
   • C) 4410 J
   • D) 7056 J
6. 6.

   A motorized winch increases the gravitational potential energy of a load by 7350 J when lifting it vertically to a height of 15.0 m. Taking the acceleration due to gravity to be $9.8\text{ m/s}^2$, what is the mass of the load?

   • A) 25 kg
   • B) 35 kg
   • C) 49 kg
   • D) 50 kg
7. 7.

   A 5.0 kg cart is moved from the bottom to the top of a ramp of length 10.0 m inclined at an angle of $30^\circ$ to the horizontal. Taking the acceleration due to gravity to be $9.8\text{ m/s}^2$, what is the gravitational potential energy gained by the cart relative to the bottom of the ramp?

   • A) 245 J
   • B) 424 J
   • C) 490 J
   • D) 49 J
8. 8.

   An object of mass 2.0 kg is held at a height of 1.5 m above the ground. If the reference level where gravitational potential energy is zero is chosen to be a balcony 4.0 m above the ground, what is the gravitational potential energy of the object relative to this reference level? (Take $g = 9.8\text{ m/s}^2$.)

   • A) -49 J
   • B) +49 J
   • C) +29.4 J
   • D) -78.4 J
9. 9.

   Two objects, P and Q, are positioned above the ground. Object P has a mass of 2.0 kg, and object Q has a mass of 6.0 kg. If the gravitational potential energy of object P relative to the ground is twice that of object Q, what is the ratio of the height of object P to the height of object Q?

   • A) 1 : 3
   • B) 3 : 1
   • C) 6 : 1
   • D) 12 : 1
10. 10.

    A crate with a mass of 4.0 kg is lifted vertically at a constant speed from a height of 1.2 m to a height of 3.7 m above the ground. Taking the acceleration due to gravity to be $9.8\text{ m/s}^2$, what is the increase in the gravitational potential energy of the crate?

    • A) 98 J
    • B) 145 J
    • C) 47 J
    • D) 49 J