Gravitational potential energy Knowledge-Based Practice

Questions

1. 1.

   Under which condition is the expression $E_p = mgh$ valid for calculating the gravitational potential energy of an object of mass $m$ at a height $h$?

   • A) When the object is moving at a constant velocity
   • B) When the gravitational field strength $g$ remains approximately constant over the height $h$
   • C) When mechanical energy is conserved and air resistance is zero
   • D) When the zero reference level is defined strictly at the centre of the Earth
2. 2.

   To which physical entity or system does gravitational potential energy strictly belong when an object is lifted near the surface of the Earth?

   • A) The lifted object alone, because its internal energy increases as it moves upward
   • B) The Earth alone, because it produces the dominant gravitational field
   • C) The surrounding atmosphere, because the vertical displacement occurs within the air
   • D) The two-body system consisting of the object and the Earth, because it arises from their mutual gravitational interaction
3. 3.

   A stone with a mass of 2.0 kg is lowered into a shaft and comes to rest at a depth of 15 m below ground level. If the ground level is defined as the zero reference level for gravitational potential energy, what is the gravitational potential energy of the stone relative to this reference? (Take the acceleration due to gravity to be 9.8 m/s2.)

   • A) +294 J
   • B) +147 J
   • C) -294 J
   • D) -147 J
4. 4.

   How does shifting the reference level where gravitational potential energy is defined to be zero affect an object's gravitational potential energy at a given height and the change in its gravitational potential energy between two heights?

   • A) The value of the gravitational potential energy at the given height changes, but the change in gravitational potential energy between the two heights remains the same.
   • B) Both the value of the gravitational potential energy at the given height and the change in gravitational potential energy between the two heights change.
   • C) The value of the gravitational potential energy at the given height remains the same, but the change in gravitational potential energy between the two heights changes.
   • D) Neither the value of the gravitational potential energy at the given height nor the change in gravitational potential energy between the two heights changes.
5. 5.

   An object is moved from a floor to a shelf along three different paths: a direct vertical lift, a gentle incline, and an irregular curved trajectory. If all three paths have the same initial and final elevations, which statement correctly compares the change in gravitational potential energy of the object along these paths?

   • A) The change is greatest for the irregular curved trajectory because the total distance traveled is largest.
   • B) The change is greatest for the direct vertical lift because the lifting force is applied purely vertically.
   • C) The change is smallest for the gentle incline because the force required to move the object is smallest.
   • D) The change is identical for all three paths because gravitational potential energy depends solely on vertical displacement.
6. 6.

   As an object of mass $m$ falls vertically through a height $h$ in a uniform gravitational field, which statement correctly describes the work done by the gravitational force and the change in the object's gravitational potential energy?

   • A) The gravitational force does negative work, and the gravitational potential energy increases by $mgh$.
   • B) The gravitational force does negative work, and the gravitational potential energy decreases by $mgh$.
   • C) The gravitational force does positive work, and the gravitational potential energy decreases by $mgh$.
   • D) The gravitational force does positive work, and the gravitational potential energy increases by $mgh$.
7. 7.

   A crate with a mass of 20 kg is moved up a 10 m long inclined ramp to reach a platform that is 3.0 m above the ground. Taking the acceleration due to gravity to be 9.8 m/s2, what is the increase in the gravitational potential energy of the crate?

   • A) 60 J
   • B) 200 J
   • C) 588 J
   • D) 1960 J
8. 8.

   Object X has a mass of $m$ and is at a height of $4h$ above the ground, while object Y has a mass of $2m$ and is at a height of $h$ above the ground. What is the ratio of the gravitational potential energy of object X to that of object Y relative to the ground?

   • A) 1 : 2
   • B) 1 : 1
   • C) 2 : 1
   • D) 4 : 1
9. 9.

   An object with a mass of 4.0 kg possesses 196 J of gravitational potential energy relative to the ground. Taking the acceleration due to gravity to be $9.8\text{ m/s}^2$, what is the height of the object above the ground?

   • A) 2.0 m
   • B) 4.0 m
   • C) 5.0 m
   • D) 8.0 m
10. 10.

    A box with a mass of 5.0 kg is raised vertically from an initial height of 1.2 m to a final height of 3.2 m above the ground. Taking the acceleration due to gravity to be $9.8\text{ m/s}^2$, what is the gain in gravitational potential energy of the box?

    • A) 49 J
    • B) 98 J
    • C) 157 J
    • D) 196 J

Answers and step-by-step solutions appear after you finish the test.