# physics

posted by .

A box of mass 5.0 kg starting from rest slides down a 1.8 m long ramp inclined at an angle of 22.0 deg. from the horizontal. If the ramp is frictionless, how long will it take the box, starting from rest, to reach the bottom of the ramp? if the frictionless ramp is replaced with a ramp having friction between the box and ramp. The time for the box to reach the bottom of the ramp is observed to double. Find the coefficient of kinetic friction between the box and the new ramp.

• physics -

1. PE=KE
PE=mgh=mg•s•sinα
KE=mv²/2
mg•s•sinα=mv²/2
v=sqrt(2g•s•sinα) =
=sqrt(2•9.8•1.8•sin22°)=3.64 m/s
v=at => a=v/t
s=at²/2= vt²/2t=vt/2
t=2s/v=2•1.8/3.64 =0.99 s
2.
t₁=2t=0.99•2=1.98 s
v₁=2s/t₁=2•1.8/1.98= 1.82 m/s

PE=KE+W(fr)
W(fr) = F(fr)s=μ•mg•cosα•s
mg•s•sinα= mv₁²/2 + μ•mg•cosα•s
μ=(g•s•sinα- v₁²/2)/ g•cosα•s=
=tanα - (v₁²/2g•cosα•s)=
=tan22°-(1.82²/2•9.8•cos22°•1.8)=0.3

## Similar Questions

1. ### physics

A wooden box with a mass of 10.0kg rests on a ramp that is inclined at an angle of 25 degrees to the horizontal. A rope attatched to the box runs parallel to the ramp and then passes over a frictionless pulley. A bucket with a mass …
2. ### Physics

Box, mass m 1 , at rest against a compressed spring, spring constant k and compression of Δx, at the top of a ramp, height h, is released. It slides down the ramp, angle θ, with friction, coefficient μ. Half way down …
3. ### physics

A box of mass 1.95 kg slides down a frictionless ramp inclined at an angle θ= 42.9 ° at constant speed. The force exerted on the box by the ramp is how many Newtons?
4. ### phyics

A box of mass 0.385 kg slides down a very smooth (frictionless) ramp which is inclined at an angle of 56.6° above the horizontal. What is the acceleration of the box down the ramp?
5. ### Physics

A box of mass 1.50 kg is given an initial velocity of 12.5 m/s up an inclined ramp that makes an angle of 25.0o with the ground, which is horizontal. The coefficient of kinetic friction between the box and the ramp is 0.240. How long …
6. ### Physics

A box of mass 1.50 kg is given an initial velocity of 12.5 m/s up an inclined ramp that makes an angle of 25.0o with the ground, which is horizontal. The coefficient of kinetic friction between the box and the ramp is 0.240. How long …
7. ### Physics

A box slides from rest down a frictionless ramp inclined at 35.0° with respect to the horizontal and is stopped at the bottom of the ramp by a spring with a spring constant of k = 3.50 104 N/m. If the box has a mass of 12.0 kg and …
8. ### Physics

A box is sitting at rest at the top of a ramp 3.00m long at an angle to the horizontal of 12 degrees. When the box reaches the bottom of the frictionless ramp, it falls an additional 2.00 m vertically before hitting the floor. How …
9. ### physics

Starting from rest, a 10kg suitcase slides down a 3.00m long ramp inclined at 30 degrees from the floor. The coefficient of friction between the suitcase and the ramp is 0.35. 1) what net force is applied to the suitcase while it is …
10. ### Physics

Starting from rest, a 10.0 Kg suitcase slides down a 3.00m long ramp inclined at 30.0 degrees from the floor. The coefficient of friction between the suitcase and ramp is .35. A: what net force is applied to suitcase while it is on …

More Similar Questions