Answer:
5.65 m
Explanation:
According to the work-energy theorem, the work (W) done on the block is equal to the change in its mechanical energy (ΔE), where the mechanical energy is the sum of its kinetic energy (KE) and gravitational potential energy (PE). The work done is equal to the net force (∑F) times the parallel distance (d). The kinetic energy is half the mass (m) times the square of the speed (v), and the potential energy is the weight (mg) times the height (h).
To find the net force, we'll draw a free body diagram, which shows all the forces acting on the block. In this case, there are four forces:
The block moves horizontally, so the net force in the vertical direction is zero.
N − mg = 0
N = mg
The net force in the horizontal direction is:
∑F = F − Nμ
∑F = F − mgμ
The work done on the block is:
W = ∑F d
W = (F − mgμ) d
The block starts and stops at rest, so the kinetic energy is zero at both places. Therefore, the work done is equal to the change in potential energy.
W = ΔPE
W = mgΔh
(F − mgμ) d = mgΔh
Δh = (F − mgμ) d / (mg)
Plugging in values:
Δh = [ 15 N − (2 kg) (9.8 m/s²) (0.2) ] (10 m) / [ (2 kg) (9.8 m/s²) ]
Δh = 5.65 m
