Question
An 85 kg person is bouncing on a bathroom scale having a force constant of 1.50 x 10^6 N/m . The amplitude of the bounce is .200 cm. What is the maximum energy stored in the spring?
Answers
GPT 3.5
To find the maximum energy stored in the spring, we can use the formula:
E = (1/2)kA²
where:
E is the maximum energy stored in the spring,
k is the force constant of the spring, and
A is the amplitude of the bounce.
Given:
k = 1.50 x 10^6 N/m
A = 0.200 cm
Converting A to meters:
A = 0.200 cm * 1 m/100 cm = 0.002 m
Substituting the given values into the formula, we have:
E = (1/2)(1.50 x 10^6 N/m)(0.002 m)²
= (1/2)(1.50 x 10^6 N/m)(0.004 m²)
= 3000 J
Therefore, the maximum energy stored in the spring is 3000 Joules.
E = (1/2)kA²
where:
E is the maximum energy stored in the spring,
k is the force constant of the spring, and
A is the amplitude of the bounce.
Given:
k = 1.50 x 10^6 N/m
A = 0.200 cm
Converting A to meters:
A = 0.200 cm * 1 m/100 cm = 0.002 m
Substituting the given values into the formula, we have:
E = (1/2)(1.50 x 10^6 N/m)(0.002 m)²
= (1/2)(1.50 x 10^6 N/m)(0.004 m²)
= 3000 J
Therefore, the maximum energy stored in the spring is 3000 Joules.