In an attempt to exercise more, Ms. Jang runs up the stairs at a constant speed. She climbs to the top of a building with a height of 24 m.

Question

a) Calculate the work done for her to reach the top if she is 62 kg.

b) If she climbs the building in 5.2 minutes, calculate the power of Ms. Jang.

c) Ms. Jang drops her calculator (150 g) from the top of the building to the ground. USING ENERGY RELATED CALCULATIONS, calculate the final velocity of the calculator, just before it hits the ground.

Answer 1

a) The work done by Ms. Jang can be calculated using the formula:

Work = Force x Distance

The force exerted by Ms. Jang can be calculated using her weight:

Force = mass x acceleration due to gravity

Using the given mass of Ms. Jang as 62 kg, and the acceleration due to gravity as 9.8 m/s²:

Force = 62 kg x 9.8 m/s² = 607.6 N

The distance she climbed is given as 24 m. Therefore, the work done is:

Work = 607.6 N x 24 m = 14582.4 J

b) Power is defined as the rate at which work is done, which can be calculated using the formula:

Power = Work / Time

The work done was calculated as 14582.4 J. The time taken to climb the building is given as 5.2 minutes, which must be converted to seconds:

Time = 5.2 minutes x 60 seconds/minute = 312 seconds

Therefore, the power of Ms. Jang is:

Power = 14582.4 J / 312 s = 46.77 W

c) To calculate the final velocity of the calculator, we can use the principle of conservation of energy. The potential energy of the calculator initially at the top of the building will be converted into kinetic energy just before it hits the ground.

The potential energy (PE) at the top of the building is given by:

PE = mass x gravitational acceleration x height

The mass of the calculator is given as 150 g, which must be converted to kg:

Mass = 150 g = 0.15 kg

The gravitational acceleration is 9.8 m/s², and the height is 24 m. Therefore, the potential energy is:

PE = 0.15 kg x 9.8 m/s² x 24 m = 35.28 J

The potential energy will be converted into kinetic energy just before the calculator hits the ground. The equation for kinetic energy (KE) is:

KE = 0.5 x mass x velocity²

The mass is still 0.15 kg, and the final velocity is unknown. Therefore, we need to solve for velocity. Rearranging the equation gives:

velocity = √(2 x KE / mass)

Substituting the potential energy calculated earlier:

velocity = √(2 x 35.28 J / 0.15 kg)

velocity ≈ √(470.4 m²/s²) ≈ 21.7 m/s

Therefore, the final velocity of the calculator just before it hits the ground is approximately 21.7 m/s.