Gravitational potential energy Transitional Reasoning Download PDF

Questions

1. 1.

   A grid-scale gravity energy storage facility uses an electric hoist to lift solid modular blocks vertically to store surplus electrical energy as gravitational potential energy. The facility aims to store a net gravitational potential energy of 19.6 MJ by lifting a collection of blocks through a vertical height of 25 m in a uniform gravitational field of 9.8 N/kg. If the hoisting system operates with an overall efficiency of 80%, what total mass of blocks must be raised, and what total electrical energy must be supplied to the hoist?

   • A) 80 000 kg and 24.5 MJ
   • B) 80 000 kg and 15.7 MJ
   • C) 784 000 kg and 24.5 MJ
   • D) 784 000 kg and 15.7 MJ
2. 2.

   An engineering team tests a 20 kg prototype delivery cart on an inclined test track. The cart is released from rest at a height of 5.0 m above the horizontal floor and travels down the slope. During the descent, friction between the wheels and track performs -180 J of work on the cart. Setting the floor as the reference level where gravitational potential energy is zero and taking the gravitational field strength as 9.8 N/kg, what is the kinetic energy of the cart when it reaches the floor?

   • A) 980 J
   • B) 800 J
   • C) 1160 J
   • D) 180 J
3. 3.

   A sports biomechanics team launches a 0.40 kg test projectile from ground level with an initial speed of $v_0$ at an elevation angle of $60^\circ$ above the horizontal. Air resistance is negligible throughout the flight, and the ground is chosen as the reference level where gravitational potential energy is zero. At the highest point of its trajectory, what percentage of the projectile's total mechanical energy is stored as gravitational potential energy?

   • A) 25%
   • B) 75%
   • C) 50%
   • D) 87%
4. 4.

   During an atmospheric survey, a research drone carries a 2.5 kg sensor package vertically upward from a launch platform at an elevation of 150 m to an observation altitude of 750 m. Throughout the ascent, the gravitational field strength is uniform at 9.8 N/kg, and aerodynamic drag is monitored separately. What is the work done on the sensor package by the gravitational force, and what is the corresponding change in the gravitational potential energy of the sensor–Earth system?

   • A) The work done by gravity is +14.7 kJ, and the change in gravitational potential energy is +14.7 kJ.
   • B) The work done by gravity is -14.7 kJ, and the change in gravitational potential energy is -14.7 kJ.
   • C) The work done by gravity is -14.7 kJ, and the change in gravitational potential energy is +14.7 kJ.
   • D) The work done by gravity is +14.7 kJ, and the change in gravitational potential energy is -14.7 kJ.
5. 5.

   Two identical vertical cylindrical tanks standing on horizontal ground are connected at their bases by a closed valve. Initially, Tank 1 contains a fluid of mass $m$ filled to a depth $h$, while Tank 2 is completely empty. Once the valve is opened, the fluid redistributes until both tanks reach an equilibrium depth of $\frac{h}{2}$. Taking the ground as the reference level where potential energy is zero, what is the net change in the gravitational potential energy of the fluid system?

   • A) $-\frac{1}{4} m g h$
   • B) $-\frac{1}{2} m g h$
   • C) $0$
   • D) $+\frac{1}{4} m g h$
6. 6.

   A construction crane pivots a uniform structural beam of mass 400 kg and length 6.0 m from a flat horizontal position on the ground to an upright vertical position. The thickness of the beam is negligible compared to its length, and the ground serves as the zero-potential-energy reference level. Taking the gravitational field strength as 9.8 N/kg, what is the gravitational potential energy of the beam once it is fully upright?

   • A) 23,520 J, because the entire mass is treated as being at the maximum vertical height of 6.0 m.
   • B) 15,680 J, because two-thirds of the beam's mass determines the effective vertical elevation.
   • C) 11,760 J, because the center of mass of the uniform beam is elevated to a height of 3.0 m.
   • D) 3,920 J, because the potential energy is equivalent to the gravitational force acting on the beam.
7. 7.

   A building design team is evaluating the energy efficiency of a counterweighted elevator system. The elevator car has a mass of 1200 kg and travels upward by 15 m at a constant speed, while a connected 1000 kg counterweight simultaneously descends by 15 m. Taking the gravitational field strength as 9.8 N/kg, what is the net change in the gravitational potential energy of the two-object system during this movement?

   • A) An increase of 176.4 kJ
   • B) An increase of 29.4 kJ
   • C) An increase of 323.4 kJ
   • D) A decrease of 29.4 kJ
8. 8.

   During a mining safety inspection, a 5.0 kg monitoring module is moved vertically downward from an upper ledge to a lower platform that is 12 m lower. Analyst X sets the reference level of zero gravitational potential energy at the upper ledge, whereas Analyst Y sets the reference level at the floor of the mine, 20 m below the lower platform. Taking the gravitational field strength as 9.8 N/kg, which statement correctly compares the gravitational potential energy calculations made by the two analysts?

   • A) Analyst Y calculates a larger decrease in gravitational potential energy because the module possesses a greater total elevation above Analyst Y's chosen zero level.
   • B) Both analysts determine identical initial and final gravitational potential energies because potential energy depends solely on the mass and vertical displacement.
   • C) Analyst X determines that the change in gravitational potential energy is negative, whereas Analyst Y determines that it is positive because the module remains above Analyst Y's zero reference level.
   • D) Both analysts determine the exact same change in gravitational potential energy of $-588\text{ J}$, even though their calculated initial and final potential energy values differ.
9. 9.

   A field technician transports a container of mass 25 kg from a baseline valley station to a summit observation deck located at a vertical elevation of 40 m above the station. The technician evaluates Route X, a direct 50 m path, and Route Y, a winding 120 m path with variable slopes. Assuming a uniform gravitational field strength of 9.8 N/kg, what is the change in the container's gravitational potential energy, and how does the route taken affect this value?

   • A) It increases by 12,250 J along Route X and by 29,400 J along Route Y, because gravitational potential energy is directly proportional to the total distance traversed.
   • B) It increases by 9,800 J along Route X, but the value cannot be calculated for Route Y because gravitational potential energy requires a constant angle of inclination.
   • C) It increases by 29,400 J along Route Y and 12,250 J along Route X, because greater mechanical work against gravity is always accumulated along longer pathways.
   • D) It increases by 9,800 J along both routes, because gravitational potential energy depends solely on vertical displacement and is independent of the path taken.
10. 10.

    An engineering team evaluates the energy requirements of a vertical warehouse lift. Payload 1 has a mass of 80 kg and is raised from Floor 1 at a height of 2.0 m to Floor 3 at a height of 11.0 m. Payload 2 has a mass of 120 kg and is raised from Floor 2 at a height of 5.0 m to Floor 3 at a height of 11.0 m. Assuming the gravitational field strength $g$ is uniform, which statement correctly compares the gain in gravitational potential energy of the two payloads?

    • A) Payload 2 gains 1.5 times as much gravitational potential energy as Payload 1 because its mass is 50% greater.
    • B) Both payloads gain the same amount of gravitational potential energy because the product of their mass and vertical displacement is equal.
    • C) Payload 1 gains 1.5 times as much gravitational potential energy as Payload 2 because its vertical displacement is 1.5 times larger.
    • D) Payload 2 gains more gravitational potential energy than Payload 1 because its final gravitational potential energy relative to the ground is greater.