1. [1pt] A professor of mass m = 65 kg is seated on a light harness connected to a rope and pulley system as shown. The...

1. [1pt]
A professor of mass m = 65 kg is seated on a light harness connected to a rope and pulley system as shown. The professor's feet touch a uniform plank of mass m_plank = 20 kg which is supported by a hinge at the wall. A mass M in a light bucket is suspended from the right end of the plank. The professor is a distance ℓ = 2.90 m from the hinge; the plank has length L = 6.20 m.

1. Are you kidding? This situation cannot be in equilibrium for any values of M.
2. If the plank remains horizontal, the concept of static equilibrium can be used to calculate the tension in the rope.
3. The tension in the rope leads to a torque of magnitude TL on the plank, taken about the hinge.
4. If M = 0 and the plank remains horizontal, the tension in the rope does not depend on the ratio of ℓ to L.
5. If the plank remains horizontal, the force of the professor on the plank is equal to the tension in the rope.

Answer true or false to the statements below; e.g., if the first one is true and the rest are false, enter TFFFF.

Answer:

2. [1pt]
For the values given above, find the tension in the rope if M is zero.

Answer:

3. [1pt]
What is the minimum value of M needed to make the professor just lose contact with the plank?