An object glides on a horizontal tabletop with a coefficient of kinetic friction of 0.3. If it comes to rest after 1.3 seconds, what was its initial velocity?

Question

An object glides on a horizontal tabletop with a coefficient of kinetic friction of 0.3. If it comes to rest after 1.3 seconds, what was its initial velocity?

Answer 1

Find it's acceleration by using ∑F_x = ma_x

There is only 1 force in the horizontal direction: the frictional force

F_friction = ma_x

F_norm(0.3) = ma_x

mg(0.3) = ma_x

a_x = g(0.3) = 2.94m/s²

Next use kinematics

a = (v_f - v₀)/t

Solve for v_f

Answer 2

Hey Hope, at first I thought there wasn't enough information, but this should work. The plan is to look at the forces first, to hopefully find an acceleration value. Then we can plug into our 1-d kinematics equations.

1. This object (if we neglect air friction) is undergoing 3 forces:
2. F_g going down. F_g = mg
3. F_normal from the table pointed upwards, equal and opposite to F_g. So the magnitude of F_normal is still just mg. μ
4. F_friction pulling it back. Since the other 2 cancel, F_friction is also the net force
5. Because friction is the net force, we can combine the 2 expressions, which actually makes it clear that the mass doesn't matter:
6. F_net = ma
7. F_friction = μ_k * F_normal
8. ma = μ_k * mg
9. The m's cancel, so:
10. a = .3g
11. Remember that this will actually be a negative acceleration, since friction always acts counter to the object's velocity.
12. Now we can go back to 1-d equations
13. t = 1.3s
14. a = -0.3g
15. v_f = 0m/s (it comes to rest)
16. v_i is what we're solving for
17. v_f = v_i + at
18. I'll leave the calculations to you.