University Physics I - Classical Mechanics, 2019

6.5. IN SUMMARY 127
F s,1
n
a
F s,1
k
F r,1
t
G
F E,1
Figure 6.3: Free-body diagram for block 1 in Figure 6.2, with the friction force adjusted so as to be
compatible with a nonzero acceleration to the right.
Note that I have drawn F n and the force of gravity FE,1 G as having the same magnitude, since
there is no vertical acceleration for that block. If I know the value of μ k , I should also try to draw
F k = μ k F n approximately to scale with the other two forces. Then, since I know that there is an
acceleration to the right, I need to draw F t greater than F k , since the net force on the block must
be to the right as well. And, if I were drawing a free-body diagram for block 2, I would have to
make sure that I drew its weight, FE,2 G , as being greater in magnitude than F t , since the net force
on that block needs to be downwards.
6.5 In summary
1. Whenever two objects interact, they exert forces on each other that are equal in magnitude
and opposite in direction (Newton’s 3rd law).
2. Forces are vectors, and they are additive. The total (or net) force on an object or system is
equal to the rate of change of its total momentum (Newton’s 2nd law). If the system’s mass is
constant, this can be written as F ext,all = Ma cm ,whereM is the system’s total mass and a cm
is the acceleration of its center of mass. Only the external forces contribute to this equation;
the internal forces cancel out because of point 1 above.
3. For any interaction that can be derived from a potential energy function U(x 1 − x 2 ), the
force exerted by object 2 on object 1 is equal to −dU/dx 1 (where the derivative is calculated
treating x 2 as a constant), and vice-versa.
4. The force of gravity on an object near the surface of the earth is known as the object’s weight,
and it is equal (in magnitude) to mg, wherem is the object’s inertial mass.
5. An ideal spring whose relaxed length is x 0 , when stretched or compressed to a length x, exerts
a pulling or pushing force, respectively, at both ends, with magnitude k|x − x 0 |,wherek is
called the spring constant.