A body of mass 10 kg is moving up on an inclined plane of 30^ with an acceleration 2 ~ms ⁻² . Find the force required, if the coefficient of friction between the object and the plane surface is 3 6 , [given g=10 ~ms ⁻² ].

Step-by-step solution

The forces acting on the body of mass m = 10 kg moving up the inclined plane are the applied force F (acting up the plane), the component of gravitational force mg (acting down the plane), and the frictional force f_k (acting down the plane). The equation of motion is F - mg - f_k = ma . The normal force N exerted by the plane is N = mg . The frictional force is f_k = N = mg . Given m = 10 kg, g = 10 ms ⁻² , = 30^ , a = 2 ms ⁻² , and = 3 6 . Calculating the components: mg 30^ = 10 10 1 2 = 50 N. f_k = 3 6 10 10 30^