In the gure here, a block of ice slides down a frictionless ramp at angle 6=50.0 \" while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 51.0 N and is directed up the ramp. As the block slides down through distance d = 0.490 m along the ramp, its kinetic energy increases by 83.0 J. How much greater would its kinetic energy have been if the rope had not been attached to the block? a eTextbook and Media Assistance Used Hint Assistance Used Work done by a constant force is the dot product of the force and the displacement. The component of the gravitational force along the ramp also does work during the displacement. The net work is equal to the change in the kinetic energy. Key Ideas . The work W, done by the gravitational force Fo on a particle-like object of mass m as the object moves through a displacement d is given by Wg = mgd cos 4, in which & is the angle between F , and d. . The work Wa done by an applied force as a particle-like object is either lifted or lowered is related to the work W, done by the gravitational force and the change AK in the object's kinetic energy by AK = Kf - Ki = Wa+ Wg. If Kf= Kj then the equation reduces to Wa = -Wg, which tells us that the applied force transfers as much energy to the object as the gravitational force transfers from it