- #1

garylau

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**1. Homework Statement**

A small mass m slides without friction on a surface making a quarter-‐circle with radius R, as shown. Then it lands on the top surface of a cart, mass M, that slides without friction on a horizontal surface. (In practice, this cart could be a slider on an air-‐track.) Between the top of the cart and the mass m, the coefficient of kinetic friction is µk. The mass m slides a distance d along the top of the cart, but doesn't fall off. (i) When there is no longer any relative motion between m and M, how fast is the cart.Show all working and assumptions and state carefully and explicitly any relevant laws or principles. (Hint: you will find it helpful to break the problem up into separate stages and to draw diagram for each.

**(ii) Determine how far the mass m slides along the surface of the cart before stopping on it. State explicitly any relevant laws or principles and any relevant approximations.**

## Homework Equations

mv1+Mv2=(m+M)v

F=ma 1/2mv^2=mgh

## The Attempt at a Solution

i have done the first part successfully and i try to do the second part as following

but the answer is wrong

the correct answer of the (ii) part is : d= {R(M/(m+M)µk}

when i try to use D1-D2 to get the total distance between the cart and the mass

it looks messy

**Any other way to do this question?**

thank

thank

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