# PHYSICS 221 SPRING 2013

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2 The following figure is used in Problems 28 and The potential energy for a particle of mass m is shown in the figure above. If the particle is released from rest at point G. Which regions of x are forbidden for the particle to be in? A) x B < x < x F B) x < x A and x > x G C) x C < x < x E D) Can t tell without knowing the value of m E) x < x B and x > x F 29. At which of the points labeled in the figure does the force on the particle act in the positive direction? A) F and G B) A, D, and G C) A and B D) C and E E) At no point is the force positive 30. Assume a potential energy is given by the equation U = x 2 y 2, where U is in J, and x and y are in m. What is the magnitude of the associated force, in N, at the point (x, y) = (3.0 m, 4.0 m)? A) 24 B) 96 C) 72 D) 168 E) 120

3 31. An elastic spring of (k = 98 N/m) is attached to a rigid wall at one end and to a 500 g block at the other end. The system is placed on a horizontal table and the block is pushed against the spring compressing it by 10 cm from equilibrium. The coefficient of kinetic friction between the block and the table is If the block is released, how far past the equilibrium point, in cm, will the block reach before it stops for the first time? A) 2.0 B) 4.0 C) 6.0 D) 8.0 E) Two stones, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these stones is true? A) The heavier stone will go twice as high as the lighter one because it initially had twice as much kinetic energy. B) At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy. C) At their highest point, both stones will have the same gravitational potential energy because they reach the same height. D) Both stones will reach the same height because they initially had the same amount of kinetic energy. E) The lighter stone will reach its maximum height sooner than the heavier one.

4 33. A roller coaster of mass 80 kg is moving with a speed of 30 m/s at position A as shown in the figure. The vertical height above ground level at point A is 200 m. Neglect friction. What is the speed of the coaster at point C, in m/s? A) 11 B) 23 C) 30 D) 41 E) Martha throws a 0.15 kg rubber ball down onto the floor. The ball s velocity just before impact is 6.5 m/s, and just after impact it is 3.5 m/s. If the ball is in contact with the floor for seconds, what is the magnitude of the average force applied by the floor on the ball, in N? A) 60 B) 18 C) 30 D) 120 E) 400

5 35. A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them. They are not attached to the spring. After they are released and have both moved free of the spring, which one of the following statements is true? A) The lighter block will have more kinetic energy than the heavier block. B) Both blocks will have the same amount of kinetic energy. C) The magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block. D) Both blocks will have equal speeds. E) The heavier block will have more kinetic energy than the lighter block. 36. During a snowball fight two balls with masses 0.40 and 0.60 kg, respectively are thrown at each other in a manner such that they meet head-on and combine to form a single mass. The magnitude of the initial velocity for each is 15 m/s. What is the speed of the combined snowball after the collision, in m/s? A) 15 B) 0 C) 7.5 D) 9.8 E) 3.0

6 37. In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. The collision is A) perfectly elastic B) partially inelastic C) completely inelastic D) characterized by an increase in kinetic energy E) not possible because momentum is not conserved 38. The cross-section of a uniform piece of plastic is depicted below. What is the x- position of the center of mass? A) 0.33 B) 0.75 C) 0.60 D) 0.50 E) 0.45

7 39. In the figure, a weightlifter's barbell consists of two identical uniform solid spherical masses each with radius 0.17 m and mass of 50 kg. The weights are connected by a 0.96-m uniform steel rod with a mass of 12 kg. Find the moment of inertia of the barbell, in kg-m 2, about an axis through the center and perpendicular to the rod (see figure). A) 25 B) 36 C) 44 D) 47 E) A wheel is acted on by three forces as shown in the figure. The force F 1 = 10 N acts at r = 15 cm from the center of the wheel, while F 2 = 20 N and F 3 = 15 N act at R = 30 cm from the center of the wheel. What is the magnitude of the net torque acting on the wheel, in N-m? (You can ignore any possible friction.) A) 3.0 B) 0 C) 14 D) 12 E) 6.8

8 41. A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses. A) The side the girl is sitting on will tilt downward B) It is impossible to say without knowing the distances C) The side the boy is sitting on will tilt downward D) It is impossible to say without knowing the masses E) Nothing will happen, the seesaw will still be balanced 42. A 4.6-m massless rod is loosely pinned to a frictionless pivot at point P. A 2.3-kg ball is attached to the other end of the rod (see figure). The ball is held at point A, where the rod makes a 30-degree angle above the horizontal, and is released from rest. The ball-rod assembly then swings freely in a vertical circle. What is the tension in the rod, in N, when the ball reaches the lowest point at B? A) 29 B) 107 C) 68 D) 45 E) A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), its velocity with respect to the road is A) undeterminable without knowing the radius of the tire B) 2v C) 0 D) 1.5v E) v

9 44. A ball moving horizontally at a constant speed strikes a pendulum hanging on a string from the ceiling. If the ball sticks to the pendulum, what quantities are conserved for the ball-pendulum system in this collision? A) Mechanical energy B) Total linear momentum C) Total angular momentum about the ceiling anchor D) All of the above E) None of the above 45. A wheel of radius 1.00 m is spun with a constant tangential force of 2.50 N acting at the rim (see figure). What angular displacement, in degrees, is required for this torque to do 5.90 J of work? A) 45.0 B) 75.0 C) 105 D) 135 E) A uniform solid disk of radius 1.6 m and mass 2.3 kg rolls without slipping to the bottom of an inclined plane. The inclined plane makes an angle of 10 o with the horizontal. What is the force of friction acting in the disk, in N? You may assume that the coefficient of static friction is large enough to keep the disk from slipping. A) 1.3 B) 2.6 C) 3.9 D) 5.2 E) 6.5

10 47. When you ride a bicycle in the forward direction, in what direction is the angular momentum of the wheels? A) To your left B) Backwards C) Up D) To your right E) Forwards 48. A carousel has a radius of 3.0 m and a moment of inertia of 3000 kg-m 2. The carousel is rotating unpowered and without friction with an angular velocity of 1.2 rad/s. An 80-kg man with a velocity of 5.0 m/s, on a line tangent to the rim of the carousel, as shown in the figure. When the man reaches the carousel he grabs onto the edge and hangs on. What is the final angular velocity of the carousel after the man jumps on, in rad/s? A) 0.97 B) 1.2 C) 1.3 D) 1.4 E) If the net torque on an object is zero, which one of the following statements is true? A) The object could be both rotating and accelerating linearly. B) The object cannot be rotating. C) The object is at rest. D) The forces on it also add up to zero. E) The object could be accelerating linearly but it could not be rotating.

11 50. A 70.0 kg diver stands on the edge of a uniform diving board of mass 10.0 kg and length 3.80 m. The diving board is supported at two points as shown. What is the magnitude and direction of the force at point A, in N? A) 2800 N, up B) 2010 N, up C) 784 N, up D) 2010 N, down E) 2800 N, down 51. In the figure, a 10-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 53 with the bar. The bar is uniform and weighs 40 N. How far from the hinge, in m, should a 10-kg mass be suspended for the tension T in the rope to be 125 N? A) 2.3 B) 4.7 C) 6.4 D) 8.1 E) 9.5

12 52. A solid sphere of Lead has a radius of 50 cm. When it is placed at the deepest part of the ocean, the pressure is 1.1x10 8 Pa, and the radius of the sphere decreases by cm. What is the Bulk Modulus, in Pa? A) You can t determine the Bulk Modulus without knowing the density of Lead. B) 4.1x10 10 C) 1.2x10 11 D) 2.4x10 9 E) 1.1x Which one of the following statements is false? A) If two objects move closer together, the gravitational force between them increases. B) The center of gravity of an object always lies within the object. C) The moon pulls on the earth with the same magnitude force with which the earth pulls on the moon. D) The gravitational force between two objects is always attractive. E) The planets move in elliptical orbits with the Sun at one focus of the ellipse. 54. From what height above the surface of the earth, in km, should an object be dropped to initially experience an acceleration of g? The radius of the earth is m. A) 510 B) 160 C) 272 D) 554 E) 385

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