11.5 Different types of forces

We often think about friction in a negative way but very often friction is useful without us realizing it. If there was no friction and you tried to prop a ladder up against a wall, it would simply slide to the ground. Rock climbers use friction to maintain their grip on cliffs. The brakes of cars would be useless if it wasn't for friction!

Exercise

1. A 12 kg box is placed on a rough surface. A force of 20 N applied at an angle of 30 ${}^{\circ }$ to the horizontal cannot move the box. Calculate the magnitude and direction of the normal and friction forces.
2. A 100 kg crate is placed on a slope that makes an angle of 45 ${}^{\circ }$ with the horizontal. The box does not slide down the slope. Calculate the magnitude and direction of the frictional force and the normal force present in this situation.
3. What force T at an angle of 30 ${}^{\circ }$ above the horizontal, is required to drag a block weighing 20 N to the right at constant speed, if the coefficient of kinetic friction between the block and the surface is 0,20?
4. A block weighing 20 N rests on a horizontal surface. The coefficient of static friction between the block and the surface is 0,40 and the coefficient of dynamic friction is 0,20.
   1. What is the magnitude of the frictional force exerted on the block while the block is at rest?
   2. What will the magnitude of the frictional force be if a horizontal force of 5 N is exerted on the block?
   3. What is the minimum force required to start the block moving?
   4. What is the minimum force required to keep the block in motion once it has been started?
   5. If the horizontal force is 10 N, determine the frictional force.
5. A stationary block of mass 3kg is on top of a plane inclined at ${35}^{\circ }$ to the horizontal.

   

   1. Draw a force diagram (not to scale). Include the weight of the block as well as the components of the weight that are perpendicular and parallel to the inclined plane.
   2. Determine the values of the weight's perpendicular and parallel components.
   3. There exists a frictional force between the block and plane. Determine this force (magnitude and direction).
6. A lady injured her back when she slipped and fell in a supermarket. She holds the owner of the supermarket accountable for her medical expenses. The owner claims that the floor covering was not wet and meets the accepted standards. He therefore cannot accept responsibility. The matter eventually ends up in court. Before passing judgement, the judge approaches you, a science student, to determine whether the coefficient of static friction of the floor is a minimum of 0,5 as required. He provides you with a tile from the floor, as well as one of the shoes the lady was wearing on the day of the incident.
   1. Write down an expression for the coefficient of static friction.
   2. Plan an investigation that you will perform to assist the judge in his judgement. Follow the steps outlined below to ensure that your plan meets the requirements.
      1. Formulate an investigation question.
      2. Apparatus: List all the other apparatus, except the tile and the shoe, that you will need.
      3. A stepwise method: How will you perform the investigation? Include a relevant, labelled free body-diagram.
      4. Results: What will you record?
      5. Conclusion: How will you interpret the results to draw a conclusion?