Physics energy questions

Question

1.A person runs up 55 stairs of height 0.22 m. The person weighs 80 N. How much energy does it take for the person to reach the top of the stairs?

2.A block is push up a friction-less incline plane of length 11 m as seen below. The mass of the block is 28 kg and the angle of incline is 20 degrees. How much energy will in take to push the block up to the top of the incline?

3.What is the kinetic energy of a 1,993 kg car that travels at 7 m/s?

*answer and explanation please*

Answer 1

The first two questions are about Potential energy (P) created when you do work against gravity - note a that is important here is the vertical height (h) and the weight of the object W=mg. The formula is P = mgh or Wh

Problem 1: Since the height is the height of all 55 stairs you must calculate the total hight as h_total = h_{1 stair} • 55

P = mgh_total = (mg) h_total = W•(h_total)= W•(h_{1 stair} • 55)= 80 N • .22 m/stair • 55 stairs = 968 N•m =- 968 Joules

Problem 2: The inclined plane's height is the side opposite the angle in inclination so the h = l sin ø where h is height, l is the length of the of the inclined plane and ø is the angle of inclination.

P = mgh = m • g •  l sin ø = 28 kg • 9.81 m/s² • 11 m sin 20° = ... make sure you calculator is in degree mode!! ... ~ 1033 kg m/s² m = 1033 N•m = 1033 Joules

Problem 3: The third problem called for Kinetic (K) energy - the energy of motion which is calculated from mass (m) and velocity (v): K = 1/2 m v² _{= 1/2 • 1993 kg • (7 m/s)}² ~ 48,829 Joules