Cement falling into a moving trailer momentum problem

[Drizzy]

Homework Statement

a trailer with a mass of 150 kg happen to roll away with the speed 20 m/s. 450 kg cement fall staight down into the trailer! which speeds does the trailer get when the cement fall into it?

Homework Equations

[/B]
I know how to solve it but I don't know why it works. Is it because this counts as a collision?

The Attempt at a Solution

150 * 20 = V(150+450)

 

[Daeho Ro]

Where the situation is collision or merge, it satisfies
$$p_i = p_f.$$
That's it.

 

[Doc Al]

Is it because this counts as a collision?

You can think of it as a collision. Or just think of "trailer + cement" as a system whose momentum (at least horizontally) is conserved.

 

[Drizzy]

okay thanks :)

 

[stockzahn]

Homework Statement

a trailer with a mass of 150 kg happen to roll away with the speed 20 m/s. 450 kg cement fall staight down into the trailer! which speeds does the trailer get when the cement fall into it?

Homework Equations

[/B]
I know how to solve it but I don't know why it works. Is it because this counts as a collision?

The Attempt at a Solution

150 * 20 = V(150+450)

Momentum is described by a vector, because velocity is a vector. You can bilance the momenta before and after the cement fell on the trailer in two perpendicular directions (x / horizontal & y / vertical) - in both directions momentum has to be conserved.

x: m_T ⋅v_T1x + m_C ⋅v_C1x = m_T ⋅v_T2x + m_C ⋅v_C2x = 150 kg ⋅ 20 m/s + 450 kg ⋅ 0 m/s = 150 kg ⋅ v_T2x + 450 kg ⋅ v_C2x with _T2x = v_C2x

The sum of the momenta of both objects in x-direction remains the same.

y: m_T ⋅v_T1y + m_C ⋅v_C1y = m_T ⋅v_T2y + m_C ⋅v_C2y = 150 kg ⋅ 0 m/s + 450 kg ⋅ v_C1y > 150 kg ⋅ 0 + 450 kg ⋅ 0 m/s

As the momenta of the two objects can't be the same, a force must have affected them - the earth. Taking into account the momentum of Earth (assuming it was standing still, when the cement hit the trailer):

y: m_T ⋅v_T1y + m_C ⋅v_C1y + m_E ⋅v_E1y = m_T ⋅v_T2y + m_C ⋅v_C2y + m_E ⋅v_E2y = 150 kg ⋅ 0 m/s + 450 kg ⋅ v_C1y + 5.6 ⋅10²⁴ kg ⋅0 m/s = 150 kg ⋅ v_T2y + 450 kg ⋅ v_Cy2 + 5.6 ⋅10²⁴ kg ⋅ v_E2y with v_T2y = v_C2y = v_E2y

and you can calculate what's the velocity of the Earth (+ trailer + cement), due to this collision.