Phyllis Fleming Physics Physics 107
 Review - Newton's Laws
 1 An object of mass m, resting on a horizontal frictionless surface, is acted upon by an applied force F, the normal force of the surface FN, and the gravitational attraction of the earth Fg, as shown in Fig. 1 below. Find (a) Fg, (b) FN and the acceleration of the object when (c) F = 12 N and m = 2.0 kg, (d) F = 24 N and m = 2.0 kg, (e) F = 12 N and m = 1.0 kg. Take g = 10 m/s2.
 2 In Fig. 1 above, the surface now exerts a frictional force of 4.0 N on the object when it is in motion. If the mass of the object m = 2 kg, find the acceleration of the object when (a) F = 12 N and (b) F = 24 N.
 3 Two objects of mass mA = 2.0 kg and mB = 4.0 kg rests on a frictionless surface (Fig. 2 below). An applied force F = 12 N acts on object A, as shown in Fig. 2. Find (a) the acceleration of the objects, (b) the force FAB of object B on A and (c) the force FBA of object A on B.
 4 The two objects in Fig. 2 above are now connected by a massless string, string 1, and pulled to the right by exerting a force of 12 N to the right through another massless string. Find (a) the acceleration of the blocks and (b) the tension in string 1.
 5 (a) An object of mass m = 3.0 kg is set into motion and then raised with a constant velocity of 3.0 m/s. What applied force F is needed? (b) The object is now given an acceleration of 3.0 m/s2. Now what applied force is needed? Take g = 10 m/s2. See Fig. 3 below.
 6 A system, consisting of a wide rope of mass 0.10 kg between two blocks each of mass 0.10 kg, is lifted by an applied force F = 9.0 N (Fig. 4 below). (a) Find the acceleration of the system. Find the tension at (b) the top of the rope, and (c) the bottom of one-fifth of the rope. Take g = 10 m/s2.
 7 A block of mass m = 2.0 kg is moved to the right on a horizontal surface by a force of 26 N. The coefficient of kinetic friction µk between the surface and the object is 1/5. (a) Draw the object and show all of the forces acting on it. Find (b) the frictional force on the block and (c) the acceleration of the block. Take g = 10 m/s2.
 8 Repeat Problem 7 when the applied force makes an angle of 22.6o above the horizontal.
 9 An object of mass m = 3.0 kg accelerates down the frictionless inclined plane of Fig. 5 below. (a) Show all the forces acting on the object. Draw a X-axis parallel and down the plane and a Y-axis perpendicular to the plane and upward. (b) Find and draw the components of the forces on the X and Y-axes. (c) Find the acceleration of the block. Take g = 10 m/s2.
 10 Repeat Problem 9 for a coefficient of kinetic friction µk between the surface and the object of 0.154.
 11 The coefficient of kinetic friction between the block of mass m1 = 2.5 kg and the plane in Fig. 6 below is 1/6. Find (a) the acceleration of the block and (b) the tension in the string. Take g = 10 m/s2.
 12 An object of mass m = 2 kg moves in a circle on a table with uniform circular motion. The speed of the object is 2 m/s and the radius of the circle is 0.5 m. Find the (a) frictional force acting on the object and (b) total force of the table on the object.
 13 A wooden rod of negligible mass is connected to the shaft of a motor. An object with mass m = 2 kg is attached to the other end of the rod. As the shaft rotates, the object moves in a vertical circle of radius 0.5 m with a constant speed of magnitude v = 3 m/s. (a) Find the magnitude of the centripetal acceleration for this object. The vertical circular path is shown in Fig. 7 below for an object that moves counterclockwise. Redraw the figure and show on it, the direction of the velocity at (b) B, the bottom of the circle, (c) T, the top of the circle and (d) S, the side of the circle. Now draw the direction of the acceleration for points (e) B, (f) T and (g) S. Find the force of the rod on the object For for points (h) B, (i) T and (j) S.
 14 A simple pendulum consists of a point object (called a bob) of mass m at the end of a massless string of length L. When the string is vertical, the bob is at its equilibrium position. When it goes to the right a restoring force tends to return it to the equilibrium position. When it goes to the left, the restoring force again tends to return it to the equilibrium position. (a) Isolate the object and show all the forces that act on it. (b) Taking the X-axis tangent to the path and the Y-axis in toward the center of the arc (Fig. 8 below), write equations for (Fnet)x = max and (Fnet)y = max, with the correct forces or a component of a force under (Fnet)x and (Fnet)y. Find (c) ax and the tension in the string when the bob is (i) at its maximum displacement and (ii) the equilibrium position.
 15 A small object of mass m is suspended from a string of length L. The object revolves in a horizontal circle of radius r with constant speed v, as in Fig. 9 below. Since the string sweeps out the surface of a cone, the system is called a conical pendulum. (a) Choose a X-axis and Y-axis for the figure and draw all of the forces acting on the object. (b) Write equations for (Fnet)x = max and (Fnet)y = max. Find (c) the speed of the object and (d) the period of revolution T.
 16 A piece of string of length L, which can support a maximum tension T, is used to whirl a particle of mass m in a circular path. What is the maximum speed with which the particle may be whirled if the circle is (a) horizontal as in Fig. 9 above or (b) vertical?
 17 The graphs shown in Fig. 10 below give information regarding the motion in the xy plane of four different particles. For each case, write equations that describe the force components Fx and Fy.
 18 A man is raising himself and the platform that he stands on with an acceleration of 5.0 m/s2 by means of the rope-and-pulley system shown in Fig. 11 below. The man's mass is 100 kg and the platform's is 60 kg.  Assume the pulley and rope are massless and neglect any tilting effects of the platform. (a) Find the tension in rope 1.  With our assumptions, T2 = T3 = T1/2.  (b) Draw separate force diagrams for the man and for the platform, label and identify each force acting on them. (c) Find the force of contact exerted by the platform on the man. Take g = 10 m/s2.
 19 Two blocks of mass m1 = 2.0 kg and m2 = 4.0 kg are pushed by an external force F = 45 N, as shown in Fig. 12 below. The coefficient of kinetic friction µk between the surface and m2 is 0.25. Find the minimum value of the coefficient of static friction µs between m2 and m1 that will prevent m1 from slipping on m2. Hint: First isolate the entire system, and then the blocks individually. Take g = 10 m/s2 .
 20 A block with a mass m will be "pinned by static friction" against the wall of a cylindrical shell that rotates about a vertical axis when it exceeds a certain critical frequency value fo. (a) Isolate the block and show all the horizontal and vertical forces acting on it. (b) Show that fo = (1/2 π)(g/µsR)1/2, where µs is the coefficient of static friction between the block and the wall of the cylinder and R is its radius (Fig. 13 below).
 21 A block with a mass m = 2.0 kg initially at rest is pushed up the incline of 37o by a horizontal force F = 60 N (Fig. 14 below). The coefficient of kinetic friction between the block and the incline µk =1/2. Find the acceleration of the block.
 22 A man of mass 60-kg pushes on a sled of mass 10-kg and the man and the sled accelerate forward with an acceleration of 2.0 m/s2. Neglect a frictional force on the sled and find (a) the force of the man on the sled, (b) the force of the sled on the man and (c) the frictional force of the snow on the man.
 23 A 10-kg object rests on a scale in an elevator. Find the reading on the scale when the elevator moves up with (a) a constant velocity of 5 m/s and (b) a constant acceleration of 5 m/s2. Take g = 10 m/s2.
 24 Two spheres of identical radii, one of lead, the other of wood fall from rest in air from a certain height. Assume the frictional force of the air is the same on both. Do the spheres have the same acceleration?

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