Question

Block 1, of mass m1 = 2.50 kg , moves along a frictionless air track with speed v1 = 27.0 m/s. It collides with block 2, of mass m2 = 33.0 kg , which was initially at rest. The blocks stick together after the collision.A. Find the magnitude pi of the total initial momentum of the two-block system. Express your answer numerically.B. Find vf, the magnitude of the final velocity of the two-block system. Express your answer numerically.C. what is the change deltaK= Kfinal- K initial in the two block systems kinetic energy due to the collision ? Express your answer numerically in joules.

Answer 1

a

The total initial momentum of the two-block system is
`p_t = 67.5 \ kg \cdot m/s^2`

b

The magnitude of the final velocity of the two-block system
`v_f = 1.9014 \ m/s`

c

the change ΔK=Kfinal−Kinitial in the two-block system's kinetic energy due to the collision is

`\Delta KE =- 847.08 \ J`

Step-by-step explanation:

From the question we are told that

The mass of first block is
`m_1 = 2.50 \ kg`

The initial velocity of first block is
`u_1 = 27.0 \ m/s`

The mass of second block is
`m_2 = 33.0\ kg`

initial velocity of second block is
`u_2 = 0 \ m/s`

The magnitude of the of the total initial momentum of the two-block system is mathematically repented as

`p_i = (m_1 * u_1 ) + (m_2 * u_2)`

substituting values

`p_i = (2.50* 27 ) + (33 * 0)`

`p_t = 67.5 \ kg \cdot m/s^2`

According to the law of linear momentum conservation

`p_i = p_f`

Where
`p_f` is the total final momentum of the system which is mathematically represented as

`p_f = (m_+m_2) * v_f`

Where
`v_f` is the final velocity of the system

`p_i = (m_1 +m_2 ) v_f`

substituting values

`67.5 = (2.50+33 ) v_f`

`v_f = 1.9014 \ m/s`

The change in kinetic energy is mathematically represented as

`\Delta KE = KE_f -KE_i`

Where
`KE_f` is the final kinetic energy of the two-body system which is mathematically represented as

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

substituting values

`KE_f = (1)/(2) (2.50 +33) * (1.9014)^2`

`KE_f =64.17 J`

While
`KE_i` is the initial kinetic energy of the two-body system

`KE_i = (1)/(2) * m_1 * u_1^2`

substituting values

`KE_i = (1)/(2) * 2.5 * 27^2`

`KE_i = 911.25 \ J`

So

`\Delta KE = 64.17 -911.25`

`\Delta KE =- 847.08 \ J`