PH112 PHYSICS II

 

CHJ                Class activity                                     WEEK II

 

  1. A 32.0-kg wheel, essentially a thin hoop with radius 1.20-m, is rotating at 280 rev/min. It must be brought to a stop in 15.0 s. a) How much work must be done to stop it? b) What is the required power?

 

  1. A tall, cylindrical-shaped chimney falls over when its base is ruptured. Treating the chimney as a thin rod with height h, express the a) radial and b) tangential components of the linear acceleration of the top of the chimney as a function of the angle q made by the chimney with the vertical. c) At what angle q does the linear acceleration equal g?

 

  1.  A wheel of radius 0.2-m is mounted on a frictionless horizontal axis. A mass less cord is wrapped around the wheel and attached to a 2.0-kg object that slides on a frictionless surface inclined at an angle of 20 degrees with the horizontal. The object slides down the incline at 2.0 m/s2. Draw the diagram for the situation along with a free body picture. What is the rotational inertia of the wheel about its axis?

 

  1. A 25.0-kg child runs at 5.00 m/s along a line tangent to the circumference of a stationary merry-go-round of radius 2.00m. If the merry-go-round has a rotational inertia of 400 kg.m2, what is the rotational rate of the merry-go-round if the child grabs hold and jumps on while going by? 

 

  1. During a jump to his partner, an aerialist is to make a triple somersault lasting a time t = 1.87 s. For the first and last quarter-revolution, he is in the extended orientation shown in the figure, with rotational inertia of 19.9 kg.m2 around his center of mass. During the rest of his flight he is in a moderate, tuck position with rotation inertia of 5.50 kg.m2. a) What must his initial angular speed around his center of mass? b) If he attempts to quadruple somersault, with the same angular velocity and time by using his a tighter tuck position what must his rotational inertia be during this tuck? c) For the quadruple somersault, what is the rotational period during the tuck?

 

  1. A student sitting on a stool can rotate freely about a vertical axis. The student, initially at rest, is holding a bicycle wheel whose rim is loaded with lead and whose rotational inertia I about the central axis is 1.5 kg.m2. The wheel is rotating at an angular speed of 3.9 rev/s. The axis of the wheel is vertical and the angular momentum of the wheel is vertically upward. The student inverts the wheel as a result the student and wheel rotate about the stool axis. The rotational inertia of the student + stool + wheel system is 6.8 k.m2. With what angular speed and direction does the student rotate? 

 

 

  1. An oscillator consists of a block of mass 0.500-kg connected to a spring. When set into oscillation with amplitude of 35.0 cm, it is observed to repeat its motion every 0.500s. Find a) the period, b) the frequency, c) the angular frequency, d) the spring constant, e) the maximum speed, and f) the maximum force exerted on the block.

 

  1. A 0.10-kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by x = 10 cm cos[(10 rad/s)t + p/2 rad]. a) What is the oscillating frequency? b) What is the maximum speed acquired by the block? At what value of x does this occur? c) What is the maximum acceleration of the block? At what value of x does this occur? d) What is the force applied to the block?

 

  1. Two blocks A (m = 1.0 kg) and B (M = 10.0 kg) and a spring (k = 200 N/m) are arranged on a horizontal, frictionless surface. Block A rests on block B and the coefficient of static friction between the blocks is 0.4. One end of the spring is connected to block B and the other end to a wall. What is the maximum amplitude of oscillation of the spring-block such that no slippage occurs between blocks A and B?