# How much work does it take to push an object with a mass of #2 kg# up a #7 m# ramp, if the ramp has an incline of #(11pi)/12 # and a kinetic friction coefficient of #8 #?

Inclination of

So,the component of weight of the object which tries to pull it down along the inclined plane is

Maximum frictional force that can act is

So,here only

So,to move the box upwards we need to apply a minimum amount of force that will be equal to the sum of maximum frictional force and downward component of the weight of the object.(as when we will try to move the object upward,frictional force will oppose the net direction of motion,so it will act downwards along the plane)

So, minimum amount of force required to move the object with constant velocity is

So,work done =

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The work done to push the object up the ramp against kinetic friction can be calculated using the formula: ( Work = mgh - \mu_k m d \cos(\theta) ), where ( m ) is mass, ( g ) is the acceleration due to gravity, ( h ) is the vertical height of the ramp, ( \mu_k ) is the kinetic friction coefficient, ( d ) is the length of the incline, and ( \theta ) is the incline angle.

Given values:

- Mass (( m )): 2 kg
- Incline angle (( \theta )): ( \frac{11\pi}{12} )
- Kinetic friction coefficient (( \mu_k )): 8
- Length of incline (( d )): 7 m

Substitute these values into the formula to find the work done.

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