Chapter 4

In a physics laboratory class, three massless ropes are tied together at a point. A pulling force is applied along each rope: \(F_{1}=150 . \mathrm{N}\) at \(60.0^{\circ}, F_{2}=200 . \mathrm{N}\) at \(100 .^{\circ}, F_{3}=100 . \mathrm{N}\) at \(190 .^{\circ} .\) What is the magnitude of a fourth force and the angle at which it acts to keep the point at the center of the system stationary? (All angles are measured from the positive \(x\) -axis.)

Four weights, of masses \(m_{1}=6.50 \mathrm{~kg}_{3}\) \(m_{2}=3.80 \mathrm{~kg}, m_{3}=10.70 \mathrm{~kg},\) and \(m_{4}=\)

4.32 A hanging mass, \(M_{1}=0.50 \mathrm{~kg}\), is attached by a light string that runs over a frictionless pulley to a mass \(M_{2}=1.50 \mathrm{~kg}\) that is initially at rest on a frictionless table. Find the magnitude of the acceleration, \(a,\) of \(M_{2}\)

A hanging mass, \(M_{1}=0.50 \mathrm{~kg}\), is attached by a light string that runs over a frictionless pulley to the front of a mass \(M_{2}=1.50 \mathrm{~kg}\) that is initially at rest on a frictionless table. A third mass \(M_{3}=2.50 \mathrm{~kg}\), which is also initially at rest on a frictionless table, is attached to the back of \(M_{2}\) by a light string. a) Find the magnitude of the acceleration, \(a,\) of mass \(M_{3}\) b) Find the tension in the string between masses \(M_{1}\) and \(M_{2}\).

A hanging mass, \(M_{1}=0.400 \mathrm{~kg}\), is attached by a light string that runs over a frictionless pulley to a mass \(M_{2}=1.20 \mathrm{~kg}\) that is initially at rest on a frictionless ramp. The ramp is at an angle of \(\theta=30.0^{\circ}\) above the horizontal, and the pulley is at the top of the ramp. Find the magnitude and direction of the acceleration, \(a_{2}\), of \(M_{2}\).

A bosun's chair is a device used by a boatswain to lift himself to the top of the mainsail of a ship. A simplified device consists of a chair, a rope of negligible mass, and a frictionless pulley attached to the top of the mainsail. The rope goes over the pulley, with one end attached to the chair, and the boatswain pulls on the other end, lifting himself upward. The chair and boatswain have a total mass \(M=90.0 \mathrm{~kg}\). a) If the boatswain is pulling himself up at a constant speed, with what magnitude of force must he pull on the rope? b) If, instead, the boatswain moves in a jerky fashion, accelerating upward with a maximum acceleration of magnitude \(a=2.0 \mathrm{~m} / \mathrm{s}^{2},\) with what maximum magnitude of force must he null on the rone?

4.39 Arriving on a newly discovered planet, the captain of a spaceship performed the following experiment to calculate the gravitational acceleration for the planet: He placed masses of \(100.0 \mathrm{~g}\) and \(200.0 \mathrm{~g}\) on an Atwood device made of massless string and a frictionless pulley and measured that it took 1.52 s for each mass to travel \(1.00 \mathrm{~m}\) from rest.

4.40 A store sign of mass \(4.25 \mathrm{~kg}\) is hung by two wires that each make an angle of \(\theta=42.4^{\circ}\) with the ceiling. What is the tension in each wire?

A crate of oranges slides down an inclined plane without friction. If it is released from rest and reaches a speed of \(5.832 \mathrm{~m} / \mathrm{s}\) after sliding a distance of \(2.29 \mathrm{~m},\) what is the angle of inclination of the plane with respect to the horizontal?

A load of bricks of mass \(M=200.0 \mathrm{~kg}\) is attached to a crane by a cable of negligible mass and length \(L=3.00 \mathrm{~m}\). Initially, when the cable hangs vertically downward, the bricks are a horizontal distance \(D=1.50 \mathrm{~m}\) from the wall where the bricks are to be placed. What is the magnitude of the horizontal force that must be applied to the load of bricks (without moving the crane) so that the bricks will rest directly above the wall?