Harry, who has a mass of 54 kg, has just gotten a flybar pogo stick and is standing on top of a small wall. He pushes off the wall with a velocity of 1.7 m/s, gets on the stick and lands. The stick has a spring constant of 3.5 x 104 N/m and he compresses it by 20.0 cm when he lands on the ground. How high was the wall he was standing on?
To find the height of the wall that Harry was standing on, we can use the principles of conservation of mechanical energy. The potential energy gained by compressing the pogo stick is equal to the potential energy lost when Harry goes up in the air, and comes back down on the ground.
Let's break down the problem step by step:
1. Calculate the potential energy gained when compressing the pogo stick:
The potential energy stored in a compressed spring is given by the equation: PE = (1/2) k x^2, where PE is the potential energy, k is the spring constant, and x is the compression distance.
Given: spring constant k = 3.5 x 10^4 N/m, compression distance x = 20.0 cm = 0.2 m.
PE = (1/2) (3.5 x 10^4 N/m) (0.2 m)^2
2. Determine the maximum height reached by Harry:
The potential energy gained when compressing the pogo stick is converted into potential energy when Harry reaches his maximum height.
The potential energy at the maximum height is given by: PE = mgh, where m is the mass of Harry, g is the acceleration due to gravity, and h is the maximum height.
Given: mass m = 54 kg, g = 9.8 m/s^2.
PE = (54 kg) (9.8 m/s^2) h
3. Set the potential energy gained equal to the potential energy lost:
Equate the potential energy gained when compressing the pogo stick to the potential energy at the maximum height:
(1/2) (3.5 x 10^4 N/m) (0.2 m)^2 = (54 kg) (9.8 m/s^2) h
4. Solve for the maximum height h:
Rearrange the equation to solve for h:
h = [(1/2) (3.5 x 10^4 N/m) (0.2 m)^2] / [(54 kg) (9.8 m/s^2)]
5. Calculate the maximum height h:
Plug in the given values to calculate the maximum height:
h = [(1/2) (3.5 x 10^4 N/m) (0.2 m)^2] / [(54 kg) (9.8 m/s^2)]
By solving this equation, you will find the height of the wall that Harry was standing on.