Question

A 4 kg billiard ball moving on a horizontal surface has a speed of 16 m/s when it strikes a horizontal coiled spring is brought to rest in a distance of 0.75 m. What is the spring constant of the spring?

Answer 1

Answer:

spring constant of the spring is 1820.44 N/m

Explanation:

given data

ball mass = 4 kg

speed = 16 m/s

distance = 0.75 m

to find out

spring constant of the spring

solution

we know that kinetic energy of ball = energy store in spring as compression

so we can express it as

0.5 × m × v² = 0.5 × k × x²    ....................1

so put here value we get spring constant k

m × v² =  k × x²

4 × 16² =  k × 0.75²

solve it we get

k  =  1820.44 N/m

so spring constant of the spring is 1820.44 N/m

Answer 2

Answer:

1820.44 N/m

Explanation:

mass of ball, m = 4 kg

velocity of ball, v = 16 m/s

distance x = 0.75 m

let k be the spring constant.

By the use of conservation of energy,

the kinetic energy of the ball is equal to the potential energy of the spring

$\frac{1}{2}mv^{2}=\frac{1}{2}kx^{2}$

4 x 16 x 16 = K x 0.75 x 0.75

K = 1820.44 N/m

Thus, the spring constant is 1820.44 N/m.