A box with an initial speed of #8 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #2/3 # and an incline of #pi /6 #. How far along the ramp will the box go?
2 Answers
The distance is
Explanation:
Taking the direction up and parallel to the plane as positive
The coefficient of kinetic friction is
Then the net force on the object is
According to Newton's Second Law
Where
The coefficient of kinetic friction is
The incline of the ramp is
The negative sign indicates a deceleration
We apply the equation of motion
Distance traveled up the ramp = 3.03087 m (after rounding off)
Explanation:
We can apply energy conservation rule here.
Initial K.E. of the box = Final P.E. of the box + energy lost due to friction
This is because initial P.E. of the box is zero as height is zero.
Also final K.E. is zero because box is finally at rest.
Suppose 'm' is the mass of box, 'u' is the initial velocity (
Initial K.E. =
Final P.E. = mgh
Energy lost due to friction = work done to overcome frictional force
=
=
Put it together to get
Cancel the common mass from both sides.
From the right angled triangle (that I am not inserting here) we get
Simplifying the equation (1) we get,
put u = 8