Physics 161, section 02
Hammer
Assignment 5
Due Oct 16, start of class
Reference reading: Still Newton’s Laws. If you’re using Knight, add Chapter 8 on Newton’s Third Law to
your reading; if you’re reading
Understanding Physics
add Chapter 6.
1)
Newton’s Third Law says that if there’s a force by object A on object B, there is at the same instant and
equal and opposite force by object B on object A. In other words, forces always come in pairs, as
symmetrical interaction between two objects. This, again, is about understanding the Newtonian
definition of force. And again, in many situations it will make perfect sense, but in some situations you
have to do a little work to reconcile it with your intuition. (That chapter by Birkett and Elby is especially
helpful on this point.) So here are a couple of questions along those lines. Explain them so they make
sense! To you!
a)
If the force is always equal and opposite, how come all games of tug-of-war don’t end in a tie? (A
game of tug of war is when two or more people stand holding opposite ends of a rope, and they
try to pull each other across a line in the middle. The side that gets pulls across the line loses.)
Because the two forces that are equal and opposite
act on different objects
. The force by A on
B is equal and opposite to the force by B on A. You don’t win a tug of war if the force you
exert on your opponent is larger than the force your opponent exerts on you — those two
forces have to be equal. You win if the force you exert on your
opponent is larger than the sum of the other forces
on your
opponent.
I stole this picture from Birkett and Elby: Note the
forces on Ben are by (1) the rope, (2) the earth (gravity), and (3)
the ground – the normal force (the ground pushing back from
being compressed) and a force of friction to the left. If the force
by the rope to the right is greater than the force by the ground to the left,
Ben will accelerate to the right. If the force by the ground to the left is
greater than the force by the rope to the right, Ben will accelerate to the
left. (I drew the tension in the rope as a little bigger in my diagram here,
so that would mean Ben’s accelerating to the right. If from there the
tension force by the rope is only equal to the friction to the left, Ben will keep moving, and
he’ll lose.) But in all cases, the force by the rope on Ben is equal to the force by Ben on the
rope.
(Some people ask me where they should draw the vectors — do you put the tail of the
vector on the object, or the head of it, and do you put it at the point of contact, etc. The
answer is it doesn’t matter: A vector has the same value wherever you draw it! But you
want to be able to keep track of which vector is which, so draw them in such a way than you
can do that…)
b)
If a baseball bat hits a baseball, how does the force of the bat on the ball compare to the force of the
ball on the bat? How can that be?