Physics 1120 --- Test  #2 --- 23 Mar 98

1. The sign in the diagram below is in the shape of a capital letter E. The sign is uniform and has a mass of 70.0 kg. It is attached to a wall by a cable and a hinge. The cable makes an angle θ = 55.0° with the wall.
   (a) Determine the location of the centre of mass of the sign. Take the hinge as being at (0,0).
   (b) Determine the tension in the cable.
   (c) Determine the horizontal and perpendicular components of the hinge force.
   
   

2. The pulley in the diagram below has a moment of inertia of I_cm = 0.55 kg-m². Two blocks are connected to the pulley at two different radii. Block #1 has a mass M₁ = 12.00 kg and is attached by a rope which is wrapped around the outside of the pulley. Block #2 has a mass M₂ = 7.00 kg and is connected to the pulley by a rope which is wrapped about its inner ring. The ropes do not slip. The outer radius of the pulley is R₁ = 0.18 m and the inner ring has radius R₂ = 0.10 m. The coefficient of kinetic friction between block #2 and the surface is µ = 0.22.
   (a) Find the angular acceleration of the pulley.
   (b) What is the acceleration of block #1?
   (c) What is the acceleration of block #2?
   
   

3. A child has removed the front wheels and axle from a toy car. The axle and wheels are shown in the diagram below. The axle has a mass of 0.100 kg, a radius of 0.005 m, and a length of 0.100 cm. Each ring shaped wheel has a mass of 0.075 kg and a radius of 0.030 m. Each wheel is connected to the axle by ten thin rods (only shown on one wheel in the diagram in the Slanted view) each of mass 0.010 kg.
   (a) Determine the moment of inertia of the wheel-axle object about an axis through the length of the axle.
   (b) The child wrapped a thin string about the axle of the object and uses the object like a yo-yo (Side view). What is the mass of the object?
   (c) What will be the acceleration of the object? (if you didn't get an answer for part a, use I = 2.079 × 10^-4 kg-m²)
   
   

4. A solid cylinder of mass M = 50.0 kg and radius R = 0.40 m is on a flat surface. A horizontal force F = 50.0 N is exerted on the axle of the cylinder as shown in the diagram below.
   (a) Which way is the static friction acting on the cylinder? Explain.
   (b) What is the acceleration of the cylinder?
   (c) Get an expression for f_s in terms of F. What is the magnitude of f_s?
   (d) If µ_s = 0.50, what is the maximum force F that can be applied before the cylinder starts slipping? (Hint - What is the maximum value of f_s?)
   
   

5. In the diagram below are two blocks with identical mass M, two pulleys of mass M_p and a spring with spring constant K. The coefficient of friction for the block on the surface is µ. The pulleys are solid disks and the rope does not slip. Initially nothing is moving and the spring is not stretched. Get an expression for the speed of the blocks when the hanging block has dropped a distance x. Your answer can only be in terms of the given quantities and constants such as g.
   
   

Questions? mike.coombes@kwantlen.ca