. In the following figure, a horizontal force of magnitude 45.0 N is applied to a 4.00-
kg book as the book slides a distance d = 0.600 m up a frictionless ramp at angle θ
= 37.00
.
a) During the displacement, what is the net work done on the book by the
gravitational and the normal forces? [1]
b) If the book has zero kinetic energy at the start of the displacement, what is its
speed at the end of the displacement?
To answer these questions, we need to consider the work done by different forces and the energy principles involved.
a) First, let's calculate the work done by the gravitational and normal forces. The gravitational force (mg) acts vertically downward, and the normal force (Fn) acts perpendicular to the ramp.
The work done by a force is given by the equation: work = force × displacement × cos(θ), where θ is the angle between the force and displacement.
In this case, the displacement is along the ramp, so the angle between the gravitational force and the displacement is 90 degrees since they are perpendicular. Therefore, the work done by the gravitational force is zero because cos(90°) = 0.
Similarly, the normal force is perpendicular to the displacement, so the angle is also 90 degrees, and the work done by the normal force is also zero.
So, the net work done on the book by the gravitational and normal forces is zero.
b) The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Since the net work done is zero, the change in kinetic energy is also zero.
Given that the book has zero kinetic energy at the start, its final kinetic energy is also zero. The kinetic energy of an object is given by the equation: kinetic energy = (1/2) × mass × velocity^2.
Since the kinetic energy is zero, we can set up the equation: 0 = (1/2) × mass × velocity^2.
Substituting the values for mass (4.00 kg) and rearranging the equation, we can solve for the velocity:
velocity = sqrt(0 / (1/2) * 4.00)
Therefore, the speed of the book at the end of the displacement is zero.