11.3 Lifts and rockets

How do rockets accelerate in space?

1. What happens to the rocket fuel?

   Gas explodes inside the rocket.

2. What effect does this have?

   This exploding gas exerts a force on each side of the rocket (as shown in the picture below of the explosion chamber inside the rocket).

   

3. What are the forces?

   Due to the symmetry of the situation, all the forces exerted on the rocket are balanced by forces on the opposite side, except for the forceopposite the open side. This force on the upper surface is unbalanced.

4. Think about the resultant force

   This is therefore the resultant force acting on the rocket and it makes the rocket accelerate forwards.

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Exercise

1. A tug is capable of pulling a ship with a force of 100 kN. If two such tugs are pulling on one ship, they can produce any force ranging from a minimum of 0 N to a maximum of 200 kN. Give a detailed explanation of how this is possible. Use diagrams to support your result.
2. A car of mass 850 kg accelerates at 2 m $·$ s ${}^{-2}$ . Calculate the magnitude of the resultant force that is causing the acceleration.
3. Find the force needed to accelerate a 3 kg object at 4 m $·$ s ${}^{-2}$ .
4. Calculate the acceleration of an object of mass 1000 kg accelerated by a force of 100 N.
5. An object of mass 7 kg is accelerating at 2,5 m $·$ s ${}^{-2}$ . What resultant force acts on it?
6. Find the mass of an object if a force of 40 N gives it an acceleration of 2 m $·$ s ${}^{-2}$ .
7. Find the acceleration of a body of mass 1 000 kg that has a 150 N force acting on it.
8. Find the mass of an object which is accelerated at 2 m $·$ s ${}^{-2}$ by a force of 40 N.
9. Determine the acceleration of a mass of 24 kg when a force of 6 N acts on it. What is the acceleration if the force were doubled and the mass was halved?
10. A mass of 8 kg is accelerating at 5 m $·$ s ${}^{-2}$ .
    1. Determine the resultant force that is causing the acceleration.
    2. What acceleration would be produced if we doubled the force and reduced the mass by half?
11. A motorcycle of mass 100 kg is accelerated by a resultant force of 500  N. If the motorcycle starts from rest:
    1. What is its acceleration?
    2. How fast will it be travelling after 20 s?
    3. How long will it take to reach a speed of 35 m $·$ s ${}^{-1}$ ?
    4. How far will it travel from its starting point in 15 s?
12. A force acting on a trolley on a frictionless horizontal plane causes an acceleration of magnitude 6 m $·$ s ${}^{-2}$ . Determine the mass of the trolley.
13. A force of 200 N, acting at 60 ${}^{\circ }$ to the horizontal, accelerates a block of mass 50 kg along a horizontal plane as shown.

    

    1. Calculate the component of the 200 N force that accelerates the block horizontally.
    2. If the acceleration of the block is 1,5 m $·$ s ${}^{-2}$ , calculate the magnitude of the frictional force on the block.
    3. Calculate the vertical force exerted by the block on the plane.
14. A toy rocket of mass 0,5 kg is supported vertically by placing it in a bottle. The rocket is then ignited. Calculate the force that is required to accelerate the rocket vertically upwards at 8 m $·$ s ${}^{-2}$ .
15. A constant force of 70 N is applied vertically to a block of mass 5 kg as shown. Calculate the acceleration of the block.

    

16. 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 (F ${}_g$ ) 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 (F ${}_{gx}$ and F ${}_{gy}$ ).
    3. Determine the magnitude and direction of the frictional force between the block and plane.
17. A student of mass 70 kg investigates the motion of a lift. While he stands in the lift on a bathroom scale (calibrated in newton), he notes three stages of his journey.
    1. For 2 s immediately after the lift starts, the scale reads 574 N.
    2. For a further 6 s it reads 700 N.
    3. For the final 2 s it reads 854 N.
    Answer the following questions:
    1. Is the motion of the lift upward or downward? Give a reason for your answer.
    2. Write down the magnitude and the direction of the resultant force acting on the student for each of the stages I, II and III.
    3. Calculate the magnitude of the acceleration of the lift during the first 2s.
18. A car of mass 800 kg accelerates along a level road at 4 m $·$ s ${}^{-2}$ . A frictional force of 700 N opposes its motion. What force is produced by the car's engine?
19. Two objects, with masses of 1 kg and 2 kg respectively, are placed on a smooth surface and connected with a piece of string. A horizontal force of 6 N is applied with the help of a spring balance to the 1 kg object. Ignoring friction, what will the force acting on the 2 kg mass, as measured by a second spring balance, be?

    

20. A rocket of mass 200 kg has a resultant force of 4000 N upwards on it.
    1. What is its acceleration in space, where it has no weight?
    2. What is its acceleration on the Earth, where it has weight?
    3. What driving force does the rocket engine need to exert on the back of the rocket in space?
    4. What driving force does the rocket engine need to exert on the back of the rocket on the Earth?
21. A car going at 20 m $·$ s ${}^{-1}$ accelerates uniformly and comes to a stop in a distance of 20 m.
    1. What is its acceleration?
    2. If the car is 1000 kg how much force do the brakes exert?