How much tension must a rope withstand if it is used to accelerate a 1000 kg car vertically upward at 0.60 m/s

Answer 1

Sum of the forces on the car = T - mg = ma

T = m (a+g)

They give you mass and a (although the units are wrong). You know g. Plugnchug.

Answer 2

f = ma = F - W; where F is the upward force (the tension) from the rope pulling on the weight W = mg of the car, m = 1000 kg, and a = .6 m/sec^2? acceleration. Solve for F = ma + W = m(a + g) = 1000(.6 + 9.81) = 1000(10.41) = 10,410 Newtons (kg-m/sec^2).

You said "accelerate" and then gave m/s units, which is velocity, not accleration. So I presumed you meant m/sec^2. If you really meant m/s, which is velocity, then F = W = 981 Newtons because the car lift would not be accelerating since f = ma = (F - W) = 0 would be true.