Newton's Third Law and Contact Forces
According to Newton's third law, isolated forces cannot exist: forces
always occur in action-reaction pairs. The contact forces between the
two blocks in this simulation are an excellent example of
action-reaction pairs.
Applied Force to the Right
Set the simulation so that the external force applied by the hand acts
in the positive direction. In this case, the external force is applied
to mass m1.
The free-body diagram for mass m1 is shown below.
Thus, m1 is acted on by two horizontal forces: the external force F to
the right, and a contact force P21 acting to the left. Newton's second
law for mass m1 gives:
Fx = F - P21 = m1a
(b) The applied force F must make both blocks accelerate. Solve this
expression for the contact force acting on mass m1.
P21 = N
Now consider mass m2.
The only horizontal force acting on this mass is the contact force
from m1: P12. Thus, Fx = P12 = m2a.
(c) Solve this for the contact force acting on m2:
P12 = N
Notice that P21 points to the left while P12 points to the right -- so
they really are different forces. Nevertheless, to within round-off
errors, you should find that their magnitudes are equal.
Applied Force to the Left
Set the simulation so that the external force applied by the hand acts
in the negative direction. In this case, the external force is applied
to mass m2.
(d) Isolate mass m2, apply Newton's second law, and solve for the contact force.
P12 = ?
(e) Isolate m1, apply Newton's second law, and solve for the contact
force acting on m1.
P21 = ?
Note that the contact force is now greater, since it must make the
heavier block accelerate.
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Exercise
Suppose that the masses in the simulation are changed so that m1 =
12.8 kg and m2 = 4 kg. Suppose also that a new external force F is
applied so that the acceleration of the two blocks is 1.88 m/s2.
(f) What is the magnitude of the applied force?
F = ?
(g) If the external force is applied in the positive direction, so
that it acts on m1, find the magnitude of the contact forces.
P21 = ?
P12 = ?
(h) If the external force is applied in the negative direction, so
that it acts on m2, find the magnitude of the contact forces.
P21 = ?
P12 = ? |
