The King's University Physics 241
Major Assignment #4

 

Please do the following questions. Each is worth 6 marks in total and some are easier than others! Show complete solutions and use, where appropriate, the techniques that we developed in class (CoM/CoE diagrams, correct notation etc)

  1. In class I often use a rotating bicycle wheel to illustrate rotational effects. The wheel has a mass of 1 kg and radius of 0.38 m. If the wheel is rotating at 40 rpm how much torque does my hand apply to stop the wheel in 0.1 s?
  2. How hot will my hand get in question #1? You will need to make some "judicious" assumptions here. Be sure to state your assumptions and conservation laws being used. Discuss whether or not your answer seems reasonable.
  3. Please complete C14R.1 from your text
  4. You are designing a parachute capable of providing a "soft landing" (v < 3 m/s) for a care package of mass 500 kg that is to be dropped in a remote area. Estimate the diameter of the parachute and discuss how you would decide on the number of support lines that you would need to attach the payload to the chute. Be sure to construct a FBD for this and justify your assumptions.(Hint: see our in-class discussion on the Tesla-S)
  5. Two children - each of mass 40 kg want to ride on a merry-go-round of mass 100 kg and radius 2 m. The children push the merry-go-round from opposite sides until it spins at a rate of 0.2 rev/s, at which point they jump on. How fast are the children running just as they jump on? If the children next move to the centre of the merry-go-round so that they are each 0.3 m from the centre how does the motion of the merry-go-round change? Give a quantitative answer please.

General Questions(10 marks)

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  1. Loop the Loop!
    1. Draw a well labeled FBD for a small solid sphere (r <<R) when it is at the top of the arc (point A) in the diagram at the right. (2 marks)
    2. Develop an expression for the speed of the sphere at point A as a function of h and R ( 3 marks).
    3. How fast is the sphere going when at point B? (2 marks)
    4. What is the minimum height h (expressed in terms of R) for which the sphere will successfully loop-the-loop? Be sure to explain your reasoning and list any assumptions that you are making. (3 marks)
  1. A box of mass m is sliding down a smooth sphere of radius R as shown on the right. Determine the angle (measured from the vertical) at which the box will leave contact with the sphere.
    1. Identify any relevant conservation laws used (2 marks)
    2. Prepare a carefully labeled FBD (3 marks)
    3. Solve for angle (5 marks)
   

Date Due:Wednesday, November 22, 2017