Question

1. A 4.00-kg mass initially moving with a velocity 3.00 x m/s on a smooth, horizontal plane is subjected to a constant force. As a result, its velocity is (8x +10y) m/s eight seconds later. Calculate the force (magnitude and direction) applied to the mass. 

2. Ron and Chuck are afloat on a calm lake attempting to tow a buoyant, 128.0-lb chest back to shore. Each of them is on his own raft, with each raft attached to the chest via ropes. As they paddle, Ron exerts a force of (-1.20x-0.40y) lb on the dest while Chuck applies a force of (-0.60x + 1.00y) lb. The chest is initially at rest at a coordinate position (-1.00 ft, 4.00 ft). Assume the forces remain constant and neglect the frictional force from the water. Calculate (a) the velocity (magnitude and direction) of the chest 10.0s after it begins to move, as well as its (b) displacement and (c) its location at this time. 

3. Consider the four scenarios of systems in static equilibrium illustrated here. Each cord pictured is massless, the surfaces smooth, and the pulleys ideal. Determine the reading on the spring scale (in newtons) for each case.

Answer 1

m=4.00kg, vi=3.00i m/s, vf=(8i+10j)m/s, Δt=8.0s

a=Δv/Δt = (vf-vi)/Δt = [(8i+10j)-(3.00i)]/8.0 = (5.00i+10j)/8.00

BY Newton’s 2^nd law,

Fnet = m*a = 4.00*[(5.00i+10j)/8.00] = 2.50i + 5.00j