A 1 lb. photo frame is placed 5 feet above the floor and another 1 lb. photo frame is placed 3 feet above the floor. Which of the following is correct?

Group of answer choices

Both frames have the same amount of potential energy.

The frame that is 3 feet above the floor has more kinetic energy than the frame that is 5 feet above the floor.

The frame that is 5 feet above the floor has more potential energy than the frame that is 3 feet above the floor.

The frame that is 3 feet above the floor has more potential energy than the frame that is 5 feet above the floor.

1 answer

To determine the potential energy of the photo frames, we can use the formula for gravitational potential energy (PE), which is given by:

\[ PE = mgh \]

where:

  • \( m \) is the mass (in pounds or in kg; note that for this calculation we will use the weight in pounds directly),
  • \( g \) is the acceleration due to gravity (approximately \( 32.2 , \text{ft/s}^2 \) when using pounds), and
  • \( h \) is the height above the reference point (floor, in this case).

Both photo frames have a weight of 1 lb. Here are their heights:

  • Frame 1: \( h = 5 \) feet
  • Frame 2: \( h = 3 \) feet

Now, let's calculate the potential energy for each frame:

For the frame 5 feet above the floor: \[ PE_1 = (1 , \text{lb}) \times (32.2 , \text{ft/s}^2) \times (5 , \text{ft}) = 1 \times 5 = 5 , \text{ft-lb} \]

For the frame 3 feet above the floor: \[ PE_2 = (1 , \text{lb}) \times (32.2 , \text{ft/s}^2) \times (3 , \text{ft}) = 1 \times 3 = 3 , \text{ft-lb} \]

Now we compare the potential energies:

  • The frame at 5 feet has 5 ft-lb of potential energy.
  • The frame at 3 feet has 3 ft-lb of potential energy.

Thus, the frame that is 5 feet above the floor has more potential energy than the frame that is 3 feet above the floor.

Therefore, the correct answer is:

The frame that is 5 feet above the floor has more potential energy than the frame that is 3 feet above the floor.