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Investigation 3
Vectors and Newton’s First and Second Laws of Motion
Vectors
1.
When two vector quantities are added together, they produce a resultant that is found using the
parallelogram rule. In the diagrams below, a and b are examples of the parallelogram rule. Use
these as a guide to find the resultant of the vectors in c and d.
a
Below is a top view of an airplane being blown off course by wind blowing in various directions.
Use the parallelogram rule to show the resulting speed and direction of travel for each case.
c
b
a
Which airplane is traveling the fastest across the ground? __________
3.
d
R
R
2.
c
b
d
How do you know?
Use the parallelogram rule in reverse to find the components of the vector R along the dashed lines.
In the diagrams below, a and b are examples. Use these as a guide to draw the components of R in c
and d.
a
c
b
R
R
d
Newton’s First and Second Laws of Motion
The motions we observe in our everyday life follow some simple rules. These rules are called Newton’s
Laws and can be expressed as follows:
First Law:
“Every object continues in a state of rest or of uniform speed in a straight line unless acted
upon by a nonzero net force.”
Second Law:
“The net force on a body equals the mass of that body times its acceleration, and the
directions of both are the same.” (net force) = (mass)x(acceleration), and the direction of
the net force is the same as the direction of the acceleration
Answer the following questions are clearly and concisely as you can.
1.
2.
A physics student holds a ball in her hand at rest.
a.
Name the two forces that are acting on the ball, and indicate the directions of the forces.
b.
The two forces must have the same magnitude but must be in opposite directions so that the
ball is at rest. Which one of Newton’s Laws tells us this?
The physics student releases the ball (lets the ball drop). Consider the ball as it falls toward the
ground without air resistance.
a.
Is the ball accelerating? If it is, then in what direction is its acceleration?
b.
Which one of Newton’s Laws applies to this situation?
c.
What does Newton’s Second Law say about the direction of the “net force” acting on the object
and the direction of the acceleration?
d.
Name the force (or forces) that is (are) acting on the ball as it is falling, and indicate its (their)
direction(s).
3.
A physics student who weighs 800 Newtons (about 170 lbs) stands on a bathroom
scale in an elevator that is not moving (at rest).
a.
What two forces are acting on him, i.e., what forces does he feel? How are the
strengths of the two forces related to each other? Which one of Newton’s laws
applies here?
forces:
strengths:
Newton’s Law:
b.
On the diagram of the student in the elevator above, draw two vectors to represent the two
forces acting on the student. (Remember that vectors represent both the direction and the
magnitude of forces.)
In the following questions, you should think first about the type of motion – is the object stationary (at
rest) or traveling at a constant velocity (uniform speed in a straight line), or is the object undergoing an
acceleration? This will tell you whether Newton’s First Law or Newton’s Second Law applies.
4.
Refer to the situation in question 3. For the following motions of the elevator, indicate whether the
reading on the bathroom scale is the same as, greater than, or less than the reading when the elevator
was stationary, and indicate the directions of the “net force” on the student as up, down or no net
force. Also indicate the direction of the acceleration according to Newton’s Second Law as up, down,
or no acceleration.
elevator motion
bathroom scale
reading
“net force” direction*
not moving
begins to move
upward
no acceleration
>800 Newtons
moving upward with
constant velocity
no net force
slows as it reaches the
top floor
starts downward from
the top floor
slows as it reaches the
bottom floor
acceleration direction*
downward
<800 Newtons
upward
*Remember that the direction of the net force and the acceleration are the same.
5.
A physics student sitting in a stationary Lamborghini (car), is holding onto the steering wheel, and is
strapped in with her seat belt. She knows that in the vertical direction, the gravitational force pulls
her downward and the seat pushes her upward and that the net vertical force is zero, thus resulting in no
upward or downward acceleration. In the horizontal direction, the back of the seat pushes her forward
and the steering wheel pushes her backward.
Compare the strengths of the two horizontal forces -- the back of the seat pushing her forward and
the steering wheel pushing her backward (which one is greater, or are they the same?) when
she accelerates away from a stop sign
she travels on a straight road at 120 mph
she slows because she hears a CHP siren