# A Block Sliding Across the Floor

1. Feb 28, 2012

### Jamesdynasty

1. The problem statement, all variables and given/known data

A box slides across a frictionless floor with an initial speed v = 3.2 m/s. It encounters a rough region where the coefficient of friction is µk = 0.1. If instead the strip is only 1.56734693877551 m long, with what speed does the box leave the strip?

2. Relevant equations

3. The attempt at a solution

2. Feb 28, 2012

### dipole

Well firstly, you've measured the length of the strip to less than the diameter of an atom! Stick with something like 1.57m, any more precision than that is unnecessary.

What you want to do is use the equation for the force of friction and calculate what it should be given the coefficient of friction. You can use the definition of work, W = ∫Fdx to calculate how much work the Friction force will do, and realize that this energy is lost. Then, using conservation of energy calculate what the new kinetic energy of the box should be, and solve for the velocity.

3. Feb 28, 2012

### Jamesdynasty

still a little confused

4. Feb 29, 2012

### ehild

Can you calculate the force of friction? If you feel confused about the mass of the box, just take it 1 kg. When you know the force, find the acceleration.

If you learnt about energy you can use dipole's hint. Calculate the work of the friction (how do you get the work?) and the work done is equal to the change of kinetic energy.

Or apply the kinematic laws.
The acceleration (deceleration really) is constant. What do you know about "motion with uniform acceleration" ? What are the equations for the velocity and displacement?

ehild

5. Mar 9, 2012

### Staff: Mentor

Based on zero effort by Jamesdynasty, this thread is closed.