Dynamics problem solving in physics class usually involves difficultcalculations that take into account a number of vectors on a free-bodydiagram.
SAT II Physics won’t expect you to make any difficultcalculations, and the test will usually include the free-body diagramsthat you need. Your task will usually be to interpret free-bodydiagrams rather than to draw them.
Example 1
The Three Stooges are dragging a 10 kg sled across a frozen lake. Moe pulls with force M, Larry pulls with force L, and Curly pulls with force C. If the sled is moving in the 
direction,and both Moe and Larry are exerting a force of 10 N, what isthemagnitude of the force Curly is exerting? Assuming that frictionisnegligible, what is the acceleration of the sled? (Note: sin 30 =cos60 = 0.500 and sin 60 = cos 30 = 0.866.)
The figure above gives us a free-bodydiagram that shows us the direction in which all forces are acting, butwe should be careful to note that vectors in the diagram are not drawnto scale: we cannot estimate the magnitude of
C simply by comparing it to
M and
L.
What is the magnitude of the force Curly is exerting?
Since we know that the motion of the sled is in the
direction, the net force,
M +
L +
C, must also be in the
direction. And since the sled is not moving in the
direction, the
y-component of the net force must be zero. Because the
y-component of Larry’s force is zero, this implies:
where
is the
y-component of
M and
is the
y-component of
C. We also know:
If we substitute these two equations for
and
into the equation
, we have:
What is the acceleration of the sled?
According to Newton’s Second Law, the acceleration of the sled is
a =
F/m. We know the sled has a mass of 10 kg, so we just need to calculate the magnitude of the net force in the
-direction.
Now that we have calculated the magnitude of thenet force acting on the sled, a simple calculation can give us thesled’s acceleration:
We have been told that the sled is moving in the
direction, so the acceleration is also in the
direction.
This example problem illustrates the importanceof vector components. For the SAT II, you will need to break vectorsinto components on any problem that deals with vectors that are not allparallel or perpendicular. As with this example, however, the SAT IIwill always provide you with the necessary trigonometric values.
Example 2
Each of the following free-body diagrams shows the instantaneous forces,
F, acting on a particle and the particle’s instantaneous velocity,
v. All forces represented in the diagrams are of the same magnitude.
1.In which diagram is neither the speed nor the direction of the particle being changed?
2. In which diagram is the speed but not the direction of the particle being changed?
3. In which diagram is the direction but not the speed of the particle being changed?
4. In which diagram are both the speed and direction of the particle being changed?
The answer to question 1 is
B. Thetwo forces in that diagram cancel each other out, so the net force onthe particle is zero. The velocity of a particle only changes under theinfluence of a net force. The answer to question 2 is
C. Thenet force is in the same direction as the particle’s motion, so theparticle continues to accelerate in the same direction. The answer toquestion 3 is
A. Because the force is acting perpendicular tothe particle’s velocity, it does not affect the particle’s speed, butrather acts to pull the particle in a circular orbit. Note, however,that the speed of the particle only remains constant if the forceacting on the particle remains perpendicular to it. As the direction ofthe particle changes, the direction of the force must also change toremain perpendicular to the velocity. This rule is the essence ofcircular motion, which we will examine in more detail later in thisbook. The answer to question 4 is
D. The net force on theparticle is in the opposite direction of the particle’s motion, so theparticle slows down, stops, and then starts accelerating in theopposite direction.
[
本帖最后由 端木·宇 于 2008-6-19 20:07 编辑 ]
