Mechanics Questions Circular Motion Question 1 An object of mass 450g moves in a circular path of radius 15m.
It completes 25 revolutions per second. Calculate a) the angular velocity b) the linear speed of the object c) the magnitude of the force needed to maintain this motion d) the work done by this force during 10 revolutions. Question 2 A mass of 15kg is moving in a circular path at the end of a metal rod 4m long. The axis of rotation passes through the other end of the rod and the plane of the motion is horizontal. The maximum tension that the rod can tolerate is 5 104N. a) Draw a diagram showing the force(s) acting on the mass. Ignore the force of gravity and assume there are no frictional forces. b) Indicate clearly on the diagram the direction in which the mass will move if the rod breaks. c) Calculate the maximum linear speed with which the mass can move without breaking the rod. d) Calculate the maximum rotational frequency. Question 3 Now consider a situation similar to the one described in the previous question but this time we have a rod 8m long with a mass of 15kg on each end. The axis of rotation now passes through the middle of the rod. What is the maximum rotational frequency in this case (assuming the rod can still take a maximum of 5 104N tension).
Question 4 A 200g mass is moving in a circular path on the end of a light metal rod 05m long. The axis of rotation passes through the other end of the rod and the plane of the motion is vertical. The rotational frequency is 12s-1. a Calculate the angular velocity of the mass. ) b Draw two diagrams showing the positions of the mass when the tension ) in the rod is i) maximum and ii) minimum. Label the forces acting on the mass and explain briefly why the tension varies. c Calculate the magnitudes of the maximum and minimum tensions. ) d Calculate the angular velocity at which the minimum tension is zero. ) Question 5 A body of mass 2kg is attached to a string 1m long and moves in a horizontal circle of radius 50cm, as shown below. (This arrangement is often called a "conical pendulum".) a) Calculate the magnitude of the tension in the string. b Calculate the time period of the motion. ) Question 6
a ) b )
At what angle should a rod surface be banked in order that a vehicle can go round a bend of radius 55m at a speed of 40 kmh-1? Suppose that a vehicle attempts to go round this bend at 100 kmh-1. If the coefficient of friction between the wheels of the vehicle and the road surface is 025, and the mass of the vehicle is 15tons, will the vehicle skid or not? Show your calculations.
Sample Problem #1
A 900-kg car moving at 10 m/s takes a turn around a circle with a radius of 25.0 m. Determine the acceleration and the net force acting upon the car. The solution of this problem begins with the identification of the known and requested information. Known Information: Requested Information:
m = 900 kg a = ???? v = 10.0 m/s Fnet = ???? R = 25.0 m To determine the acceleration of the car, use the equation a = v2 / R. The solution is as follows: a = v2 / R a = (10.0 m/s)2 / (25.0 m) a = (100 m2/s2) / (25.0 m) a = 4 m/s2 To determine the net force acting upon the car, use the equation Fnet = ma. The solution is as follows. Fnet = m a Fnet = (900 kg) (4 m/s2) Fnet = 3600 N
Sample Problem #2
A 95-kg halfback makes a turn on the football field. The halfback sweeps out a path that is a portion circle with a radius of 12-meters. The halfback makes a quarter of a turn around the circle in 2.1 seco Determine the speed, acceleration and net force acting upon the halfback. The solution of this problem begins with the identification of the known and requested information. Known Information: m = 95.0 kg R = 12.0 m Traveled 1/4-th of the circumference in 2.1 s Requested Information: v = ???? a = ???? Fnet = ????
To determine the speed of the halfback, use the equation v = d / t where the d is one-fourth of the circumference and the time is 2.1 s. The solution is as follows: v=d/t v = (0.25 2 pi R) / t v = (0.25 2 3.14 12.0 m) / (2.1 s) v = 8.97 m/s To determine the acceleration of the halfback, use the equation a = v2 / R. The solution is as follows: a = v2 / R a = (8.97 m/s)2 / (12.0 m) a = (80.5 m2/s2) / (12.0 m) a = 6.71 m/s2 To determine the net force acting upon the halfback, use the equation Fnet = ma. The solution is as follows. Fnet = m*a = (95.0 kg)*(6.71 m/s2)
Fnet Fnet = 637 N
