PROBLEM 2 10 points. [ ] increases [ ] decreases [ ] stays the same. Briefly justify your answer:

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1 PROBLEM 2 10 points A disk of mass m is tied to a block of mass 2m via a string that passes through a hole at the center of a rotating turntable. The disk rotates with the turntable at a distance R from the center of the turntable. The coefficient of static friction between the disk and the turntable is The turntable is a uniform solid disk of radius 2R and mass 10m. As long as the angular velocity of the turntable is within a certain range the disk will not slip on the surface of the turntable. Express all answers below in terms of g (the acceleration due to gravity) as well as m and/or R. [6 points] (a) If the angular velocity of the turntable is a particular value the disk rotates without sliding on the turntable with no force of friction. What is this special angular velocity ω o? [4 points] (b) If the angular velocity of the turntable is increased what happens to the tension in the string? Assume the disk still rotates with the turntable. The tension in the string: [ ] increases [ ] decreases [ ] stays the same Briefly justify your answer:

2 PROBLEM 2 10 points A wooden ball with a mass of 250 g swings back and forth on a string, pendulum style, reaching a maximum speed of 4.00 m/s when it passes through its equilibrium position. Use g = 10.0 m/s 2. [4 points] (a) What is the maximum height above the equilibrium position reached by the ball in its motion? [6 points] (b) At one instant, when the ball is at its equilibrium position and moving left at 4.00 m/s, it is struck by a bullet with a mass of 10.0 g. Before the collision the bullet has a velocity of 300 m/s to the right. The bullet passes through the ball and emerges with a velocity of 100 m/s to the right. What is the magnitude and direction of the ball s velocity immediately after the collision? Neglect any change in mass for the ball.

3 Problem 2: Circular Motion A jet airplane flies in a straight line at constant altitude and constant speed, v = 510 m/s (about 1.5 times the speed of sound). (a) Use the picture of the plane below to draw a free body diagram of the plane. Include all forces that act on the plane. (b) The plane banks into a curve while maintaining its constant speed. Draw all forces that act in the plane of the paper in the picture below. What can you say about the net force on the plane? In which direction does it point? (c) At what angle with respect to the horizontal do the wings of the plane have to bank in order to fly through a curve with radius R = 50 km at a constant speed of v = 510 m/s? (d) What is the magnitude of the total instantaneous acceleration that the pilot experiences while flying through the curve described in (c)?

4 Problem 3A: Work and Energy Consider the following experiment. A block of mass m = 1.5 kg that can slide on a surface is pushed against a spring by a force with magnitude F = 10 N, as shown in the figure below. This force, F, compresses the spring by a distance x 1 = 10 cm. There is friction between the mass and the surface it slides on. When the force F is removed, the spring expands and accelerates the mass to the right. When the spring reaches its natural length d = 12 cm, the mass separates from the spring and continues to slide on the surface for a distance x 2 = 20 cm until it comes to rest. x 1 x 2 d m F (a) Draw the free body diagram of the mass in its initial position before it is released. (b) Calculate the work done on the mass by the spring from the time the mass is released until it comes to rest a distance x 1+ x 2 further to the right. (c) Calculate the work done on the mass by friction from the time the mass is released until it comes to rest a distance x 1+ x 2 further to the right. (d) Calculate the coefficient of kinetic friction.

5 Problem 3B: Energy Conservation A ball of mass 0.50 kg is suspended vertically from a massless spring. The natural length of the spring is 0.50 m. The weight of the ball extends the spring by 0.15 m. (a) Calculate the spring constant k. (b) Now the ball is pulled down by an additional 0.20 m and released. Calculate the total mechanical energy of the ball-spring system. Assume that the potential energy of the system is zero when the spring is at its natural length. (c) The spring pulls the ball back up. Calculate the maximum height, which the ball reaches above the natural length of the spring.

6 Problem 4: Collisions A billiard ball (ball 1) moves initially along the x-axis with a speed of 2.0 m/s. It strikes another billiard ball (ball 2) of the same mass that was initially at rest. After the collision ball 1 moves at an angle of 30 o with the x-axis and ball 2 moves at an angle of +60 o with the x-axis. The mass of each of the balls is 1 kg. border 1 y v 1 v 2 60 o 2 x -30 o v 1 (e) Calculate the speed of ball 1, v 1, after the collision. (f) What is the impulse imparted on the billiard table as ball 1 then collides elastically with a border that is perpendicular to the x-axis?