Introduction and key concepts

After we have done this, we have a diagram of vectors and we simply find the sum of the vectors to get the resultant force.

For example, two people push on a box from opposite sides with forces of 4 N and 6 N respectively as shown in [link] (a). The free body diagram in [link] (b) shows the object represented by a dot and the two forces are represented by arrows with their tails on the dot.

As you can see, the arrows point in opposite directions and have different lengths. The resultant force is 2 N to the left. This result can be obtained algebraically too, since the two forces act along the same line. First, as in motion in one direction, choose a frame of reference. Secondly, add the two vectors taking their directions into account.

For the example, assume that the positive direction is to the right, then:

Remember that a negative answer means that the force acts in the opposite direction to the one that you chose to be positive. You can choose the positive direction to be any way you want, but once you have chosen it you must keep it.

As you work with more force diagrams in which the forces exactly balance, you may notice that you get a zero answer (e.g. 0 N). This simply means that the forces are balanced and that the object will not accelerate.

Once a force diagram has been drawn the techniques of vector addition introduced in Vectors can be used. Depending on the situation you might choose to use a graphical technique such as the tail-to-head method or the parallelogram method, or else an algebraic approach to determine the resultant. Since force is a vector quantity all of these methods apply.

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Exercise

1. A force acts on an object. Name three effects that the force can have on the object.
2. Identify each of the following forces as contact or non-contact forces.
   1. The force between the north pole of a magnet and a paper clip.
   2. The force required to open the door of a taxi.
   3. The force required to stop a soccer ball.
   4. The force causing a ball, dropped from a height of 2 m, to fall to the floor.
3. A book of mass 2 kg is lying on a table. Draw a labeled force diagram indicating all the forces on the book.
4. A boy pushes a shopping trolley (mass 15 kg) with a constant force of 75 N. A constant frictional force of 20 N is present.
   1. Draw a labeled force diagram to identify all the forces acting on the shopping trolley.
   2. Draw a free body diagram of all the horizontal forces acting on the trolley.
   3. Determine the resultant force on the trolley.
5. A donkey (mass 250 kg) is trying to pull a cart (mass 80 kg) with a force of 400 N. The rope between the donkey and the cart makes an angle of 30 ${}^{\circ }$ with the cart. The cart does not move.
   1. Draw a free body diagram of all the forces acting on the donkey.
   2. Draw a force diagram of all the forces acting on the cart.
   3. Find the magnitude and direction of the frictional force preventing the cart from moving.