Question

Imagine that a person is seated in a chair that is suspended by a rope that goes over a pulley. The person holds the other end of the rope in his or her hands. Assume that the combined mass of the person and chair is M.
What is the magnitude of the downward force the person must exert on the rope to raise the chair at a constant speed? Express your answer in terms of M and g. (Hint: the answer is not Mg!)
What is the magnitude of the required force if the person is accelerating upward with mag(a ⃑)=0.10g? 

Answer 1

The tension in the rope acts upwards with respect to the chair and upwards with respect to the force of the man's hands. Both tension forces are equal and in the same direction. Ma=-Mg+tension1+tension2. Tension 1 and 2 are equal so the equation reads Ma=-Mg+2tension so Ma+Mg=2F(t) so M(a+g)/2=F. The chair moves at a constant speed so acceleration is zero implying 1/2(Mg)=F(t).