# 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

#### Answer:

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

#### Answer:

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