Question

An 89.0 kg fullback moving east with a speed of 5.6 m/s is tackled by an 85.0 kg opponent running west at 2.84 m/s, and the collision is perfectly inelastic.

(a) Calculate the velocity of the players just after the tackle. m/s
(b) Calculate the decrease in kinetic energy during the collision. J
(c) determine the mechanical energy that is lost as a result of the collision.
(d) Where did the lost energy go?

Answer 1

a.
`v_f=1.477m/s`

b. Δ
`K=1558.3J`

c.
`E_k=1034.7 J`

Step-by-step explanation:

a).

Momentum conserved

`p_(ix)=p_(fx)`

`m_1*v_1+m_2*v_2=(m_1+m_2)*v_f`

`v_f=(m_1*v_1+m_2*v_2)/(m_1+m_2)`

`v_f=(89.0kg*5.6m/s+85.0kg*-2.84m/s)/((89.0+85.0)kg)`

`v_f=1.477m/s`

b).

Δ
`K=K_i-K_f`

`(1)/(2)*m_1*v_1^2+(1)/(2)*m_2*v_2^2=(1)/(2)*(m_1+m_2)*v_f^2`

`(1)/(2)*89.0kg*(5.6m/s)^2+(1)/(2)*85.0kg*(2.84m/s)^2=(1)/(2)*(89.0+85.0)kg*(1.447m/s)^2`

Δ
`K=1558.3J`

c).

`E_k=(1)/(2)*89kg*(5.8m/s)^2-(1)/(2)*(85+89)kg*(1.44m/s)^2`

`E_k=1034.7 J`

d).

All of which has been lost as mechanical energy, and is now thermal energy warmer football players, noise a loud crunch for example.