Assignment:
Problem 1.
A) To loosen a stubborn bolt it helps to use a longer rather than a shorter wrench. Why?
B) To loosen a stubborn screw, is it better to use a screwdriver with a long thin handle or a screw driver with a short fat handle. Justify your answer.
Problem 2. Consider a merry-go-round in the shape of a uniform disc of mass 400 kg and radius 3 m. Two children each of mass 20 kg sit on the edge of the merry-go-round. A person pushes on the edge of the merry-go-round at an angle of 70 to the radial direction (20 with respect to the tangential direction.). What is the magnitude of the constant force that this must person apply to accelerate the merry-go-round from rest to an angular speed of 0.8 rad/s in a time of 2.5 seconds?
Problem 3. Two blocks are connected by a massless rope and are on opposite sides of a pulley that can rotate about an axis through its center as shown below. Let m1 = 4kg and m2 = 3 kg. Take the radius of the pulley to be R = 0.5 m and the mass of the pulley to be M = 2 kg.
A) Find the acceleration of the system if the rope slides with no friction across the pulley so that the pulley does not turn.
B) Find the acceleration of the system if the rope does not slip on the pulley, so that the pulley turns as the blocks move.
Problem 4. A sign of mass 20 kg is hung from a rod supported by a wire and a hinge as shown below. The rod is uniform and has a length of 2 m and a mass of 10 kg. The sign is hung from the center of mass of the rod.
A) Find the tension in the wire.
B) Find the force that the hinge exerts on the rod. (Find the components of the hinge force.)
Problem 5. A 100 kg diver stands at the end of a uniform 4 m long diving board of mass 40 kg. The board is supported by two pillars as shown in the gure below.. Find the force (magnitude and direction) that each support exerts on the board.
A) Estimate the energy required to launch a space probe of mass 10,000 kg if the probe is to escape from the earth.
B) How many 25-W light bulbs could be operated for one day with the energy needed to launch the space probe of part A)?
