- #1

srmico

- 16

- 1

**Hello,**

1. Homework Statement

1. Homework Statement

A spherical continuous ball is sliding with a constant velocity v along a frictionless lane. Thereafter it enters an inclined surface (the angle between the surface and the horizontal plane is α) with the coeﬃcient of friction µ between the ball and the surface.

## Homework Equations

Find the maximal height it may reach if it is known that before full stop the ball was rolling.

## The Attempt at a Solution

I solved it using energies but i get an extra dependence on velocity when the ball starts rolling, and my professor told me to repeat the exercice using torque, where the solution is nicer.

I divided the motion in two parts:

1-First the ball is sliding, when it starts going up the ramp the frictional force causes it to start rotating and lose velocity until v(t1)=wR (rolling condition).

2-From rolling until it stops at v(t2)=0

1: I use v(t1)=v(0)+at => (wR)=v(0)+at, but a depends on t as well, so I don't know how to continue.

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