2005 SPRING FINAL

Part I
Fill the following blanks (2 points for each blank):

  1. As shown in the acceleration-versus time graph of a particle, if the particle’s initial velocity is 8.0 m/s, the particle’s velocity at t = 4.0 s is 16 m/s.
  2. For the three vectors shown in the figure, A + B + C = -2i. The magnitude of vector B is 6.32.
  3. A 50,000-kg locomotive is traveling at 10 m/s when its engine and brakes both fail.  The locomotive will roll 2551 m before it comes to a stop. The coefficient of rolling friction between the wheels and the tracks is 0.002.
  4. A projectile is fired with an initial speed of 30 m/s at an angle of 60º above the horizontal. The object hits the ground 7.5 s later. The maximum height that the object reaches is 34.4 m.
  5. A 500-g ball swings in a vertical circle at the end of a 1.5-m-long string. When the ball is at the bottom of the circle, the tension in the string is 15 N. The speed of the ball at that point is 5.5 m/s
  6. The 1.0-kg block in Figure is tied to the wall with a rope. It sits on top of the 2.0-kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0-kg block is μk = 0.40. The acceleration of the 2.0-kg block is 2.16 m/s2.
  7. A 200-g ball is dropped from a height of 2.0 m, bounces on a hard floor, and rebounds to a height of 1.5 m. If the time duration between the ball hitting the ground and rebounding is 5 ms, the average impulsive force exerted on the ball is 33.6 N.
  8. The power to push a 10-kg steel block horizontally on a steel table at a steady speed of 1.0 m/s is 58.8 W.  The coefficient of kinetic friction between the block and the table is 0.60.
  9. A projectile is shot straight up from the earth’s surface at a speed of 10,000km/hr. It can go 420 km high.
  10. A 2-kg uniform thin beam is 2-m long and pivoted at one end. Two forces exerted on the beam as shown in the figure. The net torque on the beam is -30.85 Nm (CW)

Part II Problems (5 points for each problem):

  1. The spring as shown in the figure is compressed 50 cm and released to launch a 100-kg man. The track is frictionless until it starts up the incline. The coefficient of kinetic friction between the man and the incline is 0.15. (a) What is the man’s speed just after losing contact with the spring? (b) How far up the incline does he go?

    Solution.
    (a) Use conservation of energy to find the speed just after the man's losing contact with the spring:
          Kf = Uis;
          ½ mv2 = ½kx2;
          v = [(80,000 N/m)(0.50 m)2/(100 kg)]½ = 14.1 m/s.
    (b) The only nonconservative force is friction force. Use conservation of energy:
         WNC = ΔE = mgh - ½kx2;
         -μkmgcosθΔs = mgΔssinθ - ½kx2;
         -(0.15)(100 kg)(9.8 m/s2)cos30°Δs = (100 kg)(9.8 m/s2)sin30°Δs - ½(80,000 N/m)(0.50 m)2
    Solve, Δs = 16.2 m
  2. A softball player swings a bat, accelerating it from rest to 3.0 rev/s in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.
    Solution.
    Find the angular acceleration of the bat first:
    ω = ω + αt;
    (3.0 rev/s)(2π rad/rev) = 0 + α(0.2 s), α = 94.25 rad/s2
    Find the torque from
    τ = Iα = (1/3mL2)α = (1/3)(2.2 kg)(0.95 m)2(94.25 rad/s2) = 62 N·m.