Force and Acceleration

The figure below is an overhead view of a 12 kg tire that is to be pulled by three ropes. One force (Fl, with magnitude 50 N) is indicated. Orient the other two forces F2 and F3 so that the magnitude of the resulting acceleration of the tire is least, and find that magnitude if (a) F2 = 30N, F3= 20 N; (b) F2= 30 N, F3 = 10 N; and (c) F2 = F3 = 30 N.

 A weight-conscious penguin with a mass of 15.0 kg rests on a bathroom scale (see figure below). What are (a) the penguin’s weight W and (b) the normal force N on the penguin? (c) What is the reading on the scale, assuming it is calibrated in weight units?

If a nucleus captures a stray neutron, it must bring the neutron to a stop within the diameter of the nucleus by means of the strong force. That force, which “glues” the nucleus together, is essentially zero outside the nucleus. Suppose that a stray neutron with an initial speed of 1.4 X 107 m/s is just barely captured by a nucleus with diameter d = 1.0 X 10-14 m. Assuming that the force on the neutron is constant, find the magnitude of that force. The neutron’s mass is 1.67 X 10-27 kg.

Sunjamming. A “sun yacht” is a spacecraft with a large sail that is pushed by sunlight. Although such a push is tiny in everyday circumstances, it can be large enough to send the spacecraft outward from the Sun on a cost-free but slow trip. Suppose that the spacecraft has a mass of 900 kg and receives a push of 20 N.(a) What is the magnitude of the resulting acceleration? If the craft starts from rest, (b) how far will it travel in 1 day and (c) how fast will it then be moving?

A 40 kg girl and an 8.4 kg sled are on the surface of a frozen lake, 15 m apart. By means of a rope, the girl exerts a horizontal 5.2 N force on the sled, pulling it toward her. (a) What is the acceleration of the sled? (b) What is the acceleration of the girl? (c) How far from the girl’s initial position do they meet, assuming that no frictional forces act?

Two blocks are in contact on a frictionless table. A horizontal
force is applied to one block, as shown in the figure below. (a) If m1= 2.3 kg, m2 = 1.2 kg, and F = 3.2 N, find the force between the two blocks. (b) Show that if a force of the same magnitude F is applied to m2 but in the opposite direction, the force between the blocks is 2.1 N, which is not the same value calculated in (a). Explain the difference

An elevator and its load have a combined mass of 1600 kg. Find the tension in the supporting cable when the elevator, originally moving downward at 12 m/s, is brought to rest with constant acceleration in a distance of 42 m.

An object is hung from a spring balance attached to the ceiling of an elevator. The balance reads 65 N when the elevator is standing still. What is the reading when the elevator is moving upward (a) with a constant speed of 7.6 m/s and (b) with a speed of 7.6 m/s while decelerating at a rate of 2.4 m/s2?

Three blocks are connected, as shown in the figure below, on a horizontal frictionless table and pulled to the right with a force T3 = 65.0 N. If m1= 12.0 kg, m2= 24.0 kg, and m3 = 31.0 kg, calculate (a) the acceleration of the system and (b) the tensions T1 and T2 in the interconnecting cords.

An elevator weighing 6240 lb is pulled upward by a cable with an acceleration of 4.00 ft/s2. (a) Calculate the tension in the cable. (b) What is the tension when the elevator is decelerating at the rate of 4.00 ft/s2 but is still moving upward?

A chain consisting of five links, each of mass 0.100 kg, is lifted vertically with a constant acceleration of 2.50 m/s2, as shown in the figure below. Find (a) the forces acting between adjacent links,(b) the force F exerted on the top link by the person lifting the chain, and (c) the net force accelerating each link.

A 1.0 kg mass on a 37° incline is connected to a 3.0 kg mass on a
horizontal surface (see figure below). The surfaces and the pulley are frictionless. If F = 12 N, what is the tension in the connecting cord?

A block of mass m1 = 3.70 kg on a frictionless inclined plane of angle 30.0° is connected by a cord over a massless, frictionless pulley to a second block of mass m2= 2.30 kg hanging vertically (Fig. 5-52). What are (a) the magnitude of the acceleration of each block and (b) the direction of the acceleration of m2? (c) What is the tension in the cord?

A 10 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground (see figure below). (a) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground? If, after the package has been lifted, the monkey stops its climb and holds onto the rope, what are (b) the monkey’s acceleration and (c) the tension in the rope?

A hot-air balloon of mass M is descending vertically with downward acceleration a (see figure below). How much mass must be thrown out to give the balloon an upward acceleration a (same magnitude but opposite direction)? Assume that the upward force from the air (the lift) does not change because of the mass (the ballast) that is lost.

The figure below shows a man sitting in a bosun’s chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man’s hand. The combined mass of the man and chair is 95.0 kg. (a) With what force must the man pull on the rope for him to rise at constant speed? (b) What force is needed for an upward acceleration of 1.30m/s2? (c) Suppose, instead, that the rope on the right is held by a person on the ground. Repeat (a) and (b) for this new situation. (d) In each of the four cases, what is the force exerted on the ceiling by the pulley system?