Answer the following questions from the following information: A box of mass 2.0

Question

Answer the following questions from the following information: A box of mass 2.0 kg starts from rest and slides down an incline that is 1.0 m high and 2.0 m long.

a) Calculate the speed of the box at the bottom of the incline if the surface is frictionless
b) Calculate the speed of a 3.0 kg box at the bottom of the incline if the surface is frictionless
c) Calculate the speed of the 2.0 kg box if the incline has a frictional force equal to 2.0 N
d) When the 2.0 kg box gets to the bottom of the incline (with the same speed it had in the problem above), it continues its slide on a level surface and comes to rest after 4.0 m. Calculate the frictional force that causes the box to stop

Explanation / Answer

a) use conservation of energy
PE=KE
mgh=1/2mv^2
v=(2gh)=(2*2.0kg*1.0m)=2m/s

b) the velocity is the same: 2 m/s (mass cancels)

c) now energy is not conserved: friction does 2.0N*2.0m=4J of work

PE - Ff=KE

19.6J-4J=1/2mv^2

v=(2*15.6J/2kg)=3.95m/s

d) find the deceleration

vf^2=vi^2 + 2ax

a=(3.95m/s)^2/(2*4m)=-1.95m/s^2

the force is F=ma

F=(2kg*1.95m/s^2)=3.90N

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