Question

John uses an old electric pump to fill a water tank that is 8.00 meters above the ground with 1,000 kg of water. When he's finished, John notices that the pump and the air around it are hot. A device connected to the pump indicates that 102,500 J of electrical energy were consumed. Use g = 9.8 m/s².

Which of the following statements best describe the movement of energy in this system? Choose 2 answers:
A The water received 102,500 J of gravitational potential energy.
B The pump transformed 24,100 J into heat.
C The pump used 78,400 J of electrical energy.
D The water received 78,400 J of gravitational potential energy.​

Answer 1

The gravitational potential energy gained by the water is 78,400 J. The energy transformed into heat by the pump is calculated as 24,100 J, which is the difference between the total energy consumed (102,500 J) and the energy transferred to the water (78,400 J). The two correct choices are option B and D.

Step-by-step explanation:

The student's question involves understanding the transfer of energy in a system, specifically an electric pump moving water to a higher gravitational potential.

• To start, we can calculate the gravitational potential energy (GPE) gained by the water after being pumped up by using the formula GPE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height.
• In this case, m = 1,000 kg, g = 9.8 m/s², and h = 8.00 m. Therefore, the GPE gained by the water is (1,000 kg)(9.8 m/s²)(8.00 m) = 78,400 J.

• Since the total electrical energy used is given as 102,500 J, and we've established that 78,400 J of that was converted into gravitational potential energy, the rest of the energy was dissipated in other forms such as heat.
• The energy transformed into heat can be determined by subtracting the energy received by the water, 78,400 J, from the total electrical energy, yielding 102,500 J - 78,400 J = 24,100 J.