Physics 1120 In-Class Problems: Centre of Mass & Static Equilibrium

Centre of Mass

1. The distance between the oxygen molecule and each of the hydrogen atoms in a water (H₂O) molecule is 0.0958 nm; the angle between the two oxygen-hydrogen bonds is 105°. Treating the atoms as particles, find the centre of mass.
   

2. Where is the centre of mass of a uniform cubic box of side length L which has no lid?
   

3. Two uniform squares of sheet metal of dimension L × L are joined at a right angle along one edge. One of the squares has twice the mass of the other. Find the centre of mass.
   

4. A cube of iron has dimension L × L × L. A hole of radius ¼L has been drilled all the way through the cube, so that one side of the hole is tangent to one face along its entire length. Where is the centre of mass of the drilled cube?
   

5. An 80-kg logger is standing on one end of a 10-m long, 300-kg, tree trunk in the middle of the Fraser River. The logger walks upriver along the trunk to the other end of the log. As a result the log moves some distance L down river. What is the displacement L?
   

6. A shell is fired at 25 m/s at 25 above the horizontal. At the top of its parabolic flight, it breaks into two pieces. One piece, having two-thirds of the total mass of the shell lands 60 m from where the shell was fired. Where did the other piece land?

Torque and Static Equilibrium

7. In the diagram below, three forces are applied to a 3-4-5 triangle. The forces are F₁ = 91.7 N, F₂ = 150 N, and F₃ = 67.7 N. F₃ is applied at the middle of side AB. (a) Find the net torque about point A. (b) Find the net torque about point B. (c) Find the net torque about point C.
   

8. An L-shaped object of uniform density is hung over a nail so that it is free to pivot. What angle, θ, does the long side make with the vertical? The long side of the L-shaped object is twice as long as the short side?
   

9. A uniform 400 N boom is supported as shown in the figure below. Find the tension in the tie rope and the force exerted on the boon by the pin at P.
   
   

10. In the figure below, a mass of 500 kg is held motionless in the air by a 120-kg boom and a rope. Find the tension in the rope. Find the force exerted on the boom by the pin at P. The angles are θ = 30.0° and φ = 45.0°.
    

11. A rectangular sign of mass 50.0 kg and width w = 5.00 m and l = length 4.00 m is hanging from a hinge and a rope as shown in the figure below. The rope makes and angle θ = 65.0° with the right wall.
    (a) Find the tension in the rope.
    (b) Find the horizontal and vertical components of the hinge force.
    
    

12. Find the centre of mass of the object shown below. Determine the tension in the strings and the unknown angle θ. Each square has a side of length 32.0 cm. The object has a mass of 125 g.
    
    

13. The sign has a mass of 20.0 kg. The hinge is located at the bottom of the left side. Find the centre of mass. Determine the tension in the rope and the horizontal and vertical components of the hinge force. The length, l, is 12 cm.
    

14. A ladder is propped against a wall making an angle with the floor. The wall is frictionless but the coefficients of friction for the floor are μ_s and μ_k respectively. Obtain an expression for the smallest that can be if the ladder is not to slip. Recall that tanθ = sinθ/cosθ.
    
    

15. A truss is made by hinging two 3.0-m long uniform planks, each of weight 150 N, as shown below. They rest on a frictionless floor and are kept from collapsing by a tie rope. A 500 N load is held at the apex. Find the tension in the string. Hint - use symmetry to solve the problem.
    

16. A wheel of mass M and radius R rests on a horizontal surface against a step of height h (h < R). A horizontal force F applied to the axle of the wheel just raises the wheel off the step. Find the force F.
    

Problems: Chapter 7 - #5,6,7,45,46,51 & Chapter 9 - #6,15,25,27,34,35,36,42,49,50

Questions? mike.coombes@kwantlen.ca