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Illustration 4.6: Newton's Third Law, Contact Forces
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Illustration 4.6 shows graphs of position, velocity, and acceleration vs. time for a 2-kg red block (not shown to scale) pushed by a 12-N force on a frictionless horizontal surface (position is given in meters and time is given in seconds). Restart. The red block is in contact with (and therefore pushes on) the green 1-kg block (also not shown to scale). Click here to show and play the physical situation. Note that on the position vs. time graph each block's trajectory is shown in a color-coded x(t) function, while in the velocity and acceleration vs. time graphs, a single v(t) or a(t) is shown (the blocks move together and therefore must have the same velocity and acceleration). The blocks may not move together when you set the contact forces.
Now it is up to you to determine what contact forces are required to make the motion of the blocks physical. When you are ready, select the "set values and play" button with the default forces. What happens? The red block "moves through" the green one because the forces are not correct. The red block has the 12-N force acting on it and the green block has no forces acting on it. Of course each object's weight and normal force act in the vertical direction, but they cancel for each object. Here we are just considering the horizontal forces that could give a net force.
Try some values for the forces and check to see if you can get the same motion of the blocks and the same graphs as the physical situation.
Were you able to get the motion correct? Let us now go about it systematically instead of by exploring (or guessing). Show and play the physical situation with both masses as one system. If we look at things this way we have one object of mass 3 kg and a net force of 12 N, which means an acceleration of 4 m/s2 (this is borne out by the acceleration graph).
What next? We could analyze the forces acting on the first mass, but let's analyze the second mass since it has only the first mass pushing on it. Because it has an acceleration of 4 m/s2 and a mass of 1 kg, it must experience a force of 4 N from the push of the red mass. What about the red mass? Newton's third law says it must experience an equal and opposite force, here a force of -4 N. Try these values out (-4 N for the force on the red block and 4 N for the force on the green block) to see if you believe what Newton's third law says the forces should be.
Illustration authored by Anne J. Cox and Mario Belloni.
Script authored by Anne J. Cox.