Answer to Question #96637 in Mechanics | Relativity for abru

Question

A shopper is in a supermarket pushing their unladen trolley westwards across an aisle at a
constant speed of 1.4 ms-1. Another shopper with groceries in their trolley is moving north out of
the aisle at 1.8 ms-1 and the trollies collide, the shoppers releasing the trollies in surprise at the
moment of collision. The trollies jam together and end up moving at a velocity of 1.234 ms-1 in a
direction 25.7° W of N. If 41.75 J of energy is lost into noise, deforming the trolleys etc. during
the collision, what is the mass of a trolley, (assuming they are the same type of trolley) and what
was the mass of the second shopper’s groceries?

Answer 1

From the conservation of momentum:

$$m_1v_1=(m_1+m_2)v\sin{25.7\degree}$$

$$m_2v_2=(m_1+m_2)v\cos{25.7\degree}$$

$$\frac{m_1}{m_2}=\frac{v_2}{v_1}tan{25.7\degree}$$

We have:

$$0.5m_1v_1^2+0.5m_2v_2^2=0.5(m_1+m_2)v^2+E$$

$$\frac{m_1}{m_2}v_1^2+v_2^2=(1+\frac{m_1}{m_2})v^2+\frac{2E}{m_2}$$

$$\frac{1.8}{1.4}tan{25.7\degree}1.4^2+1.8^2=(1+\frac{1.8}{1.4}tan{25.7\degree})1.234^2+\frac{2(41.75)}{m_2}$$

$$m_2=42.0\ kg$$

The mass of a trolley:

$$m_1=(42.0)\frac{1.8}{1.4}tan{25.7\degree}=26.0\ kg$$

The mass of the second shopper’s groceries:

$$m_2-m_1=42.0-26.0=16.0\ kg$$