A 0.07 kg toy is made up of a spring of constant 372 N/m. When you place the toy

Question

A 0.07 kg toy is made up of a spring of constant 372 N/m. When you place the toy on the floor, cock the spring 7.0 cm and release it, the toy jumps upwards. In answering the questions,  use 10 N/m for g.

a) What is in Joules the spring potential energy stored in the toy when sitting on the floor with a cocked spring?

b) What is in Joules the mechanical energy relative to the floor of the toy when sitting on the floor with a cocked spring?

c) What is in Joules the mechanical energy relative to the floor of the toy when it is at its highest position after it jumps off the floor?

d) How high, in meters, would the toy jump to? Use two significant digits for the answer.

Explanation / Answer

(a)
Spring potential energy stored = 0.5*kx^2
Spring potential energy stored = 0.5*372*(7*10^-2)^2 J
Spring potential energy stored = 0.9114 J

(b)
Mechanical energy relative to the floor of the toy when sitting on the floor with a cocked spring = 0.9114 J
(c)
At Highest Position , All the Spring Potential Energy will be Converted to Gravitational Potential Energy, Therefore
Mechanical energy relative to the floor of the toy when it is at its highest position after it jumps off the floor = 0.9114 J

(d)
m*g*h = Potential Energy Stored in String.
0.07*10*h = 0.9114
h = 1.302 m
Height toy would jump , h = 1.302 m

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