Answer:
To find the magnitude of the force applied to the box, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the box is initially at rest, so its initial kinetic energy is zero. Therefore:
Work done = Change in kinetic energy
The work done by the student is 60 J, and the change in kinetic energy is equal to the final potential energy of the box, which is given by:
Potential energy = mgh
where m is the mass of the box, g is the acceleration due to gravity, and h is the height of the ramp. We can find the height of the ramp using the Pythagorean theorem:
h^2 = (500 cm)^2 + (300 cm)^2
h = 583.1 cm
Converting to meters:
h = 5.831 m
Therefore:
Potential energy = (3.0 kg)(9.8 m/s^2)(5.831 m) = 170.42 J
So we have:
60 J = 170.42 J - 0 J
The force applied to the box can be found using the formula for work:
Work = Force x Distance x Cosine of angle
where the angle is the angle between the force and the displacement of the box. Since the force is applied parallel to the ramp, the angle is 0 degrees and the cosine is 1. Therefore:
Force = Work / Distance
where the distance is the length of the ramp, which is 500 cm = 5.0 m. Substituting the values we have:
Force = 60 J / 5.0 m = 12 N
Therefore, the magnitude of the force applied to the box is 12 N.
The total amount of work done by the student is the sum of the work done in the two displacements. Therefore:
Total work = 300 J + 400 J = 700 J
So the answer is not given in the options provided.