0.2 Force, momentum and impulse  (Page 19/35)

Exercise

1. The diagram shows an object of weight W, attached to a string. A horizontal force F is applied to the object so that the string makes an angle of $\theta$ with the vertical when the object is at rest. The force exerted by the string is T. Which one of the following expressions is incorrect?

   

   1. A F + T + W = 0
   2. B W = T cos $\theta$
   3. C tan $\theta$ = $\frac{F}{W}$
   4. D W = T sin $\theta$
2. The point Q is in equilibrium due to three forces $F_1$ , $F_2$ and $F_3$ acting on it. Which of the statements about these forces is INCORRECT?
   1. A The sum of the forces $F_1$ , $F_2$ and $F_3$ is zero.
   2. B The three forces all lie in the same plane.
   3. C The resultant force of $F_1$ and $F_3$ is $F_2$ .
   4. D The sum of the components of the forces in any direction is zero.

   

3. A point is acted on by two forces in equilibrium. The forces
   1. A have equal magnitudes and directions.
   2. B have equal magnitudes but opposite directions.
   3. C act perpendicular to each other.
   4. D act in the same direction.
4. A point in equilibrium is acted on by three forces. Force $F_1$ has components 15 N due south and 13 N due west. What are the components of force $F_2$ ?

   

   1. A 13 N due north and 20 due west
   2. B 13 N due north and 13 N due west
   3. C 15 N due north and 7 N due west
   4. D 15 N due north and 13 N due east
5. 1. Define the term 'equilibrant'.
   2. Two tugs, one with a pull of 2500 N and the other with a pull of 3 000 N are used to tow an oil drilling platform. The angle between the two cables is 30  ${}^{\circ }$ . Determine, either by scale diagram or by calculation (a clearly labelled rough sketch must be given), the equilibrant of the two forces.
6. A 10 kg block is held motionless by a force F on a frictionless plane, which is inclined at an angle of 50 ${}^{\circ }$ to the horizontal, as shown below:

   

   1. Draw a force diagram (not a triangle) indicating all the forces acting on the block.
   2. Calculate the magnitude of force F. Include a labelled diagram showing a triangle of forces in your answer.
7. A rope of negligible mass is strung between two vertical struts. A mass M of weight W hangs from the rope through a hook fixed at point Y
   1. Draw a vector diagram, plotted head to tail, of the forces acting at point Y. Label each force and show the size of each angle.
   2. Where will the tension be greatest? Part P or Q? Motivate your answer.
   3. When the tension in the rope is greater than 600N it will break. What is the maximum mass that the above set up can support?

   

8. An object of weight $w$ is supported by two cables attached to the ceiling and wall as shown. The tensions in the two cables are $T_1$ and $T_2$ respectively. Tension $T_1=1200$  N. Determine the tension $T_2$ and weight $w$ of the object by accurate construction and measurement or calculation.

   

9. A rope is tied at two points which are 70 cm apart from each other, on the same horizontal line. The total length of rope is 1 m, and the maximum tension it can withstand is 1000 N. Find the largest mass (m), in kg, that can be carried at the midpoint of the rope, without breaking the rope. Include a labelled diagram showing the triangle of forces in your answer.

   

Forces between masses

In Grade 10, you saw that gravitational fields exert forces on masses in the field. A field is a region of space in which an object experiences a force. The strength of a field is defined by a field strength. For example, the gravitational field strength, $g$ , on or near the surface of the Earth has a value that is approximately 9,8 m $·$ s ${}^{-2}$ .