Question

1. 7. if a spring stretches 0.25 m under a force of 5 n, find the spring constant.

• hint: use f = k * x.

1. 8. a spring with k = 80 n/m is compressed by 0.15 m. what is the force?

• hint: use f = k * x.

1. 9. find the potential energy in a spring with k = 80 n/m and x = 0.3 m.

• hint: use pe = 1/2 k x².

1. 10. a spring stores 1.6 j of energy when stretched 0.2 m. what is the spring constant?

• hint: use pe = 1/2 k x².

1. 11. what force is needed to stretch a spring with k = 25 n/m by 0.4 m?

• hint: use f = k * x.

1. 12. a spring is compressed by 0.2 m and stores 0.5 j of energy. find the spring constant.

• hint: use pe = 1/2 k x².

1. 13. if a spring has a spring constant of 70 n/m, how much force is needed to stretch it 0.3 m?

• hint: use f = k * x.

1. 14. calculate the energy stored in a spring with k = 45 n/m and x = 0.25 m.

• hint: use pe = 1/2 k x².

1. 15. a spring stretches 0.1 m under a force of 2 n. what is the spring constant?

• hint: use f = k * x.

1. 16. find the force needed to compress a spring with k = 90 n/m by 0.2 m.

• hint: use f = k * x.

1. 17. a spring stores 3.6 j of energy when stretched 0.4 m. what is the spring constant?

• hint: use pe = 1/2 k x².

1. 18. how much energy is stored in a spring with k = 20 n/m and x = 0.5 m?

• hint: use pe = 1/2 k x².

Explanation:

7.

Step1: Rearrange Hooke's law formula

Given $F = kx$, we can solve for $k$ as $k=\frac{F}{x}$.

Step2: Substitute values

Substitute $F = 5N$ and $x=0.25m$ into the formula, so $k=\frac{5}{0.25}$.

Step1: Apply Hooke's law

Use the formula $F = kx$, where $k = 80N/m$ and $x = 0.15m$.

Step2: Calculate force

$F=80\times0.15$.

Step1: Apply potential - energy formula

Use the formula $PE=\frac{1}{2}kx^{2}$, with $k = 80N/m$ and $x = 0.3m$.

Step2: Calculate potential energy

$PE=\frac{1}{2}\times80\times(0.3)^{2}$.

Answer:

$20N/m$

10.