# A box with an initial speed of #3 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #1/3 # and an incline of #( pi )/3 #. How far along the ramp will the box go?

##### 2 Answers

Here,as the tendency of the block is to move upwards,hence the frictional force will act along with the component of its weight along the plane to decelerate its motion.

So,net force acting downwards along the plane is

So,net deceleration will be

So,if it moves upward along the plane by

So,

The distance is

#### Explanation:

Resolving in 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 of Motion

Where

So

The coefficient of kinetic friction is

The acceleration due to gravity is

The incline of the ramp is

The acceleration is

The negative sign indicates a deceleration

Apply the equation of motion

The initial velocity is

The final velocity is

The acceleration is

The distance is