Question

A .183 kg ball is moving 18.8 m/s when it runs into a spring of spring constant 86.9 N/m. How much KE does the ball have when it has compressed the spring 0.520 m? (Unit=J)

Answer 1

The value is
`KE_B = 20.59 \ J`

Step-by-step explanation:

From the question we are told that

The mass of the ball is
`m = 183 \ kg`

The initial speed of the ball is
`u = 18.8 \ m/s`

The spring constant is
`k = 86.9 \ N/m`

The compression distance is
`x = 0.520 \ m`

Generally the energy stored in the string is mathematically represented as

`E = (1)/(2) * k * x^2`

=>
`E = (1)/(2) * 86.9 * 0.520 ^2`

=>
`E = 11.75 \ J`

Generally the kinetic energy of the ball is mathematically represented as

`KE_b = (1)/(2) * m * u^2`

=>
`KE_b = (1)/(2) * 0.183 * (18.8 )^2`

`KE_b = 32.34 \ J`

Generally the KE the ball have when it has compressed the spring is mathematically represented as

`KE_B = KE_b - E`

=>
`KE_B = 32.34 - 11.75`

=>
`KE_B = 20.59 \ J`