# A box with an initial speed of #1 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #3/4 # and an incline of #pi /8 #. How far along the ramp will the box go?

##### 2 Answers

#### Answer:

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

Here,downward component of the weight of the box which tries to pull it down along the plane is

And,maximum value of kinetic frictional force that can act is

Now, initially,the box has a tendency to go up,so frictional force will act along with the downward component of its weight to stop the motion.

So,net acceleration downwards will be

So,if it goes up by

Or,

After that the block will come to momentary rest and try to move down due to its downwards component of weight,but maximum frictional force value is more than that,so it will keep the block at rest at that point.