# Ball rolling down a ramp, no slipping, + friction (conceptual question)

• B
So if a ball is rolling down a ramp and not slipping, you have two torques... the mg*sin(theta) portion of gravity and the (mu)mgcos(theta) for friction. My question is this: Does this friction force remove energy from the ball? (I know it affects the balls rotation but this is just changing forms of energy) My teacher did a problem in class where we wanted to know the final velocity of the ball at the end of the ramp and I subtracted the work due to friction FD. Was I wrong to do this and if so why (my teacher said it was wrong but couldn't say why uggh)? Thanks so much guys

## Answers and Replies

rcgldr
Homework Helper
Usually static friction isn't considered as a force that performs work, since there's no movement between surfaces at the point of contact. If a flat bed truck is accelerating on a level road with a box on the flat bed without sliding so that the box accelerates at the same rate as the truck, then from the ground frame of reference the work performed on the box equals the friction force (between flat bed and box) times the distance traveled with respect to the ground, but the source of energy is the trucks engine, not friction force.

Back to the ball rolling down a ramp, if you calculated the "work done" related to friction, that should equal the gain in angular kinetic energy of the ball, but the source of that energy is gravity, not the friction force. The total energy of the ball increases by m g h (mass, gravity, height of ramp), some of it linear kinetic energy, some of it angular kinetic energy.

thanks that's perfect

rcgldr
Homework Helper
To clarify, the method you used may not have been wrong, only referring to it as work done by friction. The total energy of the ball when it reaches the bottom of the ramp = m g h. The angular kinetic energy = friction force times distance rolled, and linear kinetic energy = total energy - angular kinetic energy. You didn't describe how you determined the friction force, which equals the angular acceleration x angular inertia / radius of ball. Angular acceleration equals linear acceleration / radius. Linear acceleration = g sin(θ) - (friction force / m). This is enough information to solve for acceleration and friction force based on θ and the angular inertia of the ball.

Does this friction force remove energy from the ball?
no friction does not change the total kinetic energy (linear + rotational) of ball
Was I wrong to do this and if so why (my teacher said it was wrong but couldn't say why uggh)?
yes you were wrong
static friction will act but net work done by static friction on body =0
since linear work = (-1)*rotational work
since (force . linear displacement) = (-1) * ( torque . angular displacement ) (. denotes scalar product operator)
so net work by friction (linear work + rotational work) = 0