Two dimensional motion

Physics 122. Problems: Two Dimensional Motion Projectile Motion

1. Look at Figure 7-1. What does it show about the time for a ball dropped straight drop and one
    falling in a downward arc to reach the ground? (Remember: horizontal and vertical motion are
    independent of each other. Sideways speed is related to some "blast-off" force while descent
    speed is due to gravity.)
3. In Figure 7-1: a) what are the initial downward velocities of the straight drop and of the arc?
    b) how would the final downward velocities of the straight drop and the arc relate to each other?
    c) how do the downward velocity of the straight drop relate to the horizontal velocity of the arc?
    d) how does the downward velocity of the arc relate to its horizontal velocity?
2. a) Look at Figure 7-2. Explain the caption.
    b) A similar situation is an object falling from a plane. To a passenger, the object falls straight
        down from the plane but to an observer on the ground, it traces an arc. Again, why?
3. In an arc:
    a) where is the only place that the final upward velocity is 0 m/s?
    b) when is the initial downward velocity = 0 m/s?
    c) where does this value occur?
    d) where is the initial upward velocity = final downward velocity?
4. Standing on a level plain, Tarzan threw a coconut at 5.7 m/s, 38⁰. Find:
    a) the velocity components, Vv, Vh.
    b) the coconut's elevation at the top of its arc.
    c) the time to reach that point.
    d) the distance it travelled downrange.
5. Baby Huey "gently" kicked a bouncer ball at 12.5 m/s, 50⁰. Redo Q. 4.
6. Flammine the Human Flaming Arrow launched herself at 6.7 m/s, 40⁰. Redo Q. 4.
7. Augustus the elephant used his trunk to launch peanuts at 9.3 m/s, 45⁰. A 3 m barrier fence is
    4 m away.
    Find:
    a) the velocity components.
    b) the time a peanut takes to reach the top of its arc.
    c) the time it would take a peanut to travel (Vh) to the fence. (Is the fence more or less than the
        half-range time away?)
    d) the elevation of a peanut when it reaches the fence. Does it cross or crash?
8. At milking time, startled by cold hands, Bessy kicks out and sends a pail flying at 5.9 m/s 57⁰.
    If a 1.2 m fence is 1.2 m away, does the pail cross or crash? Redo Q. 7.
9. The stare...the spit...the pitch...the swing! The ball is fouled up and back at 8.9 m/s, 75⁰. If the
    4 m high backstop is 3 m behind the batter, does the ball cross or crash? Redo Q. 7.
10. A jilted lover on the top of a 30 m cliff glues pics of the ex to tennis balls and serves them out
      into the ocean at 15.3 m/s, 27⁰. Find:
      a) the velocity components.
      b) the time for a ball to reach the top of its arc.
      c) the elevation of the ball above its launching point when it is at the top of its arc.
      d) the elevation of the ball above the ocean.
      e) the time for a ball to fall to the ocean.
      f) the total time a ball spends in the air.
      g) the distance the ball moves out from the cliff face (Vh).
11. An executive practicing his putting becomes frustrated and takes a swing at the golf ball sending
      it out the open 78th floor (2.5 m/floor) floor to ceiling window at 6.2 m/s, 32⁰. Redo Q. 10.
12. Elmer, wanting a new radio controlled car, sends his present car at 4.7 m/s up a 43⁰ ramp and
      over his 50th floor balcony railing. Redo Q. 10.
13. During a game of high rise golf, a ball is driven straight out at 17 m/s from a height of 65 m. Find:
      a) the time it takes the ball to descend the 65 m
      b) the time it is in the air
      c) the distance out from the face of the building it lands.
14. A youngster launches a Nerf missile at 3.7 m/s off her balcony 45 m above the ground. Redo
      Q. 13.
15. Nuggy the tourist has little sense of time and the boat leaves. Seeing Nuggette aboard, he runs
      the length of the dock and leaps out at 2.4 m/s. If the dock is 1.2 m above the boat which is
      now 4 m out from the dock, what happens?
16. An ill tempered monkey in a 25 m tree throws down a banana at 2.6 m/s, 23⁰. Find:
      a) the velocity components, Vid, Vh.
      b) the time for it to reach the ground
      c) the time it is in the air d) the distance it falls out from the foot of the tree.
17. Redo Q. 16 with a height of 40 m and a downward toss of 3.2 m/s, 30⁰.
18. Redo Q. 16 with a height of 10 m and a downward toss of 1.1 m/s, 40⁰.

Periodic Motion - Circular Motion 19. Use sketches to depict the motion of the ball in the following situation. A softball pitcher moves
      her arm in a rapid underhand arc but:
      a) releases early
      b) releases at the proper time
      c) releases late.
20. In each case in Q. 19, what is the angle between the ball's motion and the radius of the woman's
      arm swing?
21. As you spin a metal washer tied to a string around your head you can feel the outward force
      pulling your arm.
      a) What will happen to the spin radius if you reduce your muscle effort?
      b) What will happen to the washer if the string is not strong enough?
      c) Name the force that you and the string must exert to keep the spin radius the same.
      d) In what direction does this force operate?
      e) Name the acceleration caused by this force.
22. a) What centripetal acceleration is required to keep a washer on a string orbiting at 0.03 r/s in a
          1.3 m radius? Hint: change 0.03 revolutions/s into meters/s to get the speed by changing radius
          into circumference.
      b) If the washer's mass is 0.01 kg, what is the force creating the centripetal acceleration?
      c) What is the period of the orbit?
23. Redo Q. 22. if the orbit is be maintained is 3.2 m, the circular speed is 0.04 r/s and the mass is
      0.06 kg.
24. Redo Q. 22. if the orbit is be maintained is 4.6 m, the circular speed is 1.8 m/s (whew, already in m/s!)
      and the mass is 0.02 kg.
25. If there is no physical connection between the orbiting body and the center of its orbit, as is the case
      with the washer, the string and your hand, there must be something else acting to hold the object in its
      orbit. What holds a:
      a) planet on its orbit
      b) car in its path around a bend?
26. A 1 200 kg car races at 8.4 m/s around at 400 m radius track.
     a) Find its centripetal acceleration.
     b) What force causes this acceleration?
     c) Using the force from b) and the car's weight, find the µ between the track and the car's tires.
27. Redo Q. 26. if a 1 550 kg car moves at 10.3 m/s around a 1 200 m diameter (radius) track.
28. Redo Q. 26. if a 1 900 kg truck races around a 700 m radius track at 6.8 m/s. - Torque

29. What is the most effective angle for a force applied to a rigid object to create a torque?
30. Find the torque exerted by a 0.07 m long wrench on a nut when 20 N are applied its the end.
31. Find the torque exerted by a 0.09 m long wrench on a nut when 10 N are applied at a point halfway
down the handle.
32. A 20 N-m torque would be created on a nut by a 6.7 N force applied at what point on a wrench
      handle?
33. A 35 N-m torque would be created on a nut by a 7.5 N force applied at what point on a wrench
      handle?
34. At what distance from a teeter-totter pivot point should a 30 kg (weight?) child sit to balance a
      37 kg (weight?) child sitting 2.5 m from the pivot point?
35. At what distance from a teeter-totter pivot point should a 40 kg (weight?) child sit to balance a
      57 kg (weight?) child sitting 1.5 m from the pivot point?

- Simple Harmonic Motion

36. a) Look at Figure 7-15. Pulling down the weight on the spring gives the spring what type of energy?
      b) Letting go of the weight allows the spring to then change this energy into what other type?
37. During what parts of its motion does the spring show:
     a) acceleration
     b) maximum acceleration
     c) velocity
     d) maximum velocity
     e) no acceleration
     f) deceleration
     g) maximum deceleration
     h) no velocity
38. In Q. 37., which type of acceleration causes
     a) maximum velocity
     b) no velocity
39. What spring position causes
     a) maximum acceleration
     b) maximum deceleration?
40. What is the only factor affecting the swing rate of a pendulum?
41. a) Why does pulling the pendulum higher to one side before letting it go not make it have a longer
          period?
     b) Why does pulling it only a tiny bit to one side before letting it go not cause it to have a shorter
         period?
42. Find the period of a 12 cm (m ?) pendulum.
43. Find the length of a 15 s period pendulum.
44. Simple pendulum behavior occurs when the arc angle (2) is less than what?
45. Redo Q. 37 for a pendulum bob.