Hi Guys,

Need help with these couple of questions.

Q1. An empty railway cart of mass 500 kg is moving along a horizontal low-friction track at a velocity of 3.0 m s−1 due south when a 250 kg load of coal is dropped into it from a stationary container directly above it.

(a) Calculate the velocity of the railway cart immediately after the load has been emptied into it.

(b) What happens to the vertical momentum of the falling coal as it lands in the railway cart?

(c) If the fully loaded railway cart is travelling along the track at the velocity calculated in (a) and the entire load of coal falls out through a large hole in its floor, what is the final velocity of the cart?

Q2. Two iceskaters, Melita and Dean, are performing an ice dancing routine in which Dean (with a mass of 70 kg) glides smoothly at a velocity of 2.0 m s−1 due east towards a stationary Melita (with a mass of 50 kg), holds her around the waist and they both move off together. During the whole move, no significant frictional force is applied by the ice.

(a) What is Dean’s momentum before making contact with Melita?

(b) Where is the centre of mass of the system comprising Dean and Melita 3.0 s before impact?

(c) What is the velocity of the centre of mass of the system before impact?

(d) Calculate the common velocity of Melita and Dean immediately after impact.

(e) What impulse is applied to Melita during the collision?

For question 1, how are we meant to solve (a)? I used m1u1 + m2u2 = The sum of m x v, however don't know what u2 given that 1 is for the railway cart and 2 is for the coal. We need u2 to solve for v. How do I do it?

For question 2, I don't get what question (b) is asking for. What do they mean 'where is the centre of mass comprising Dean and Melita'? And for (c), are they just asking for the combined velocity before impact?

I don't want anyone to answer all the questions on this post for me, just the parts from the last 2 paragraphs above as I am unsure as to how to do it. Once I know how to do it, I should be able to do the rest by myself.

Also, it would be great if someone could answer the questions from my previous post on the physics QandA thread. It will really help me out.

All help, replies and feedback will be very much appreciated. Thanks.