lab 2; Jan 30 — velocity, acceleration

Velocity and Acceleration
Physics 111
A. Velocity: instantaneous velocity vector, v = Δx
/ Δt
.
Name:
An object is moving at a constant speed of 10.0 cm/second along the curved path below. Each of the
pairs of dots represents the object at two closely-spaced times. For example, the object is initially at
Point A, then at Point A’ an instant later. An instant after it’s at Point B it’s at Point B’.
A A’
B
B’
F
F’
G G’
X
C
C’
D
D’
E
E’
[4 pts] On each of the pairs of dots above, draw an arrow straight from A to A’, then from B to B’, etc.
Each of these short arrows is the displacement Δ x from one point to the next.
The velocity of the object is given by v = Δx
/ Δt
. Thus the velocity at Point A points in the same
direction as the Δ x arrow that starts at Point A.
[2 pts] Does the velocity at B point in the same direction as the velocity at A? yes no (circle
one)
[4 pts] Extend each arrow above until each is exactly 2.0cm long. Let each of these long arrows
represent the 10.0 cm/sec velocity of the object at each point. These are called the “instantaneous
velocity vectors” at each point.
[2 pts] Each vector that you just drew starts at one point, and has their direction determined by where
the object is just an instant later. These vectors lie along the path, parallel to the path at each location.
There's one word that describes such vectors—what is that word?
Two students have the following disagreement:
Student #1: “Why bother to try to measure the distance and time between points that are as close
together as, say, D and D’ to get the speed? I'd just pick two easy points such as D and E, measure
their separation, and calculate the velocity from there.”
Student #2: “No way norker. Look at point ‘X.’ You’re going to get the speed and the direction
wrong if you pick points that far apart.”
With which student do you agree? State your answer and explain your reasoning in the space below.
Have this
answer
checked
before
proceeding.
Velocity and Acceleration—1

Velocity and Acceleration
Physics 111
Name:
B. Acceleration: instantaneous acceleration vector, a = Δv
/ Δt
.
An object below is moving along a circular path at a constant speed of 30.0 cm/sec. The pairs of points
(A & A’, B & B’, etc.) show the object at times that are 0.10 second apart.
A’
B
B’
C
Point B is
exactly at the
top of the
circle.
A
C’
D
D’
[4 pts] You know velocities are always tangent to the path of motion. On the diagram above, draw
tangent vectors at each of the 8 points that are exactly 1.0cm long. These will represent the velocity of
the object at those points. Be careful with the directions your arrows.
[6 pts] As the object goes around this circle,
Is the magnitude of v changing? yes no (circle one)
Is the direction of v changing? yes no (circle one)
Is the total velocity v changing as the object goes around this circle? yes
no (circle one)
The velocity at point A, v A
had to change to become the velocity at point A’, v A'
. This change is the
vector Δ v AA'
, called the “change in velocity.” The vector Δ v AA'
compares the two vectors v A
and v A'
.
[10 pts] Construct the change in velocity vectors, v Δ by doing the following:
• Move the tail of v
A'
back so that it starts at Point A. Don’t change the magnitude or direction.
• Draw an arrow from the tip of the original velocity v A
to the tip of v A'
. This new arrow is
Δ v AA'
.
• Do this for the remaining 3 pairs of velocity vectors.
[2 pts] Each of the Δ v vectors points in a common direction. What is that direction?
Velocity and Acceleration—2

Physics 111
Velocity and Acceleration
Name:
Now the object is speeding up (A to A’), slowing down (B to B’), and finally just turning (C to C’).
15 mm/sec
A’
15 mm/sec
B
B’
10 mm/sec
C
10 mm/sec
The speeds of
the object are
listed next to
each point.
10 mm/sec
A
C’
10 mm/sec
[6 pts] On the diagram above, draw vectors that correctly represent the velocity of the object at each
point. To get the scale correct, if the object is moving at 10 mm/s, draw a vector that is 10 mm long; if
the object is moving at 17 mm/s, draw a vector that is 17 mm long; etc.
[10 pts] Construct the change in velocity vectors, Δ v , as before:
• Redraw v
A'
with its tail starting at Point A. Again, keep the magnitude and direction the same.
• Draw an arrow from the tip of the original velocity v A
to the tip of v A'
. This new arrow is
Δ v AA'
.
• Do this for the remaining 3 pairs of velocity vectors.
[4 pts] The object is moving at a constant speed between points C and C’. What is the angle between
Δ v CC'
and the original vector v C
?
[4 pts] The object is speeding up between points A and A’. What is the angle between Δ v AA'
and the
original vector v A
? (Hint: How does this angle compare to, say something familiar such as 90 0 ?)
[4 pts] The object is slowing down up between points B and B’. What is the angle between Δ v BB'
and
the original vector v B
?
The acceleration of an object is always in the same direction as its change in velocity, Δ v . You can see
this from the definition of acceleration: a = Δv
/ Δt
. Since this is physics, things are “always” or
“never.” In the space below, make a general rule for how the directions of the acceleration a and
velocity v tells you whether an object is only turning, if it is speeding up and turning, or if it is slowing
down and turning.
Velocity and Acceleration—3

Physics 111
C. Application: a = Δv
/ Δt
.
Velocity and Acceleration
Name:
On the previous pages you have seen that the direction of the acceleration vector can tell you whether
an object is speeding up, slowing down, or turning:
• If part of the acceleration a points in the same or opposite direction as the velocity v , then the
object will be speeding up or slowing down.
• If part of a is pointed at a 90 0 angle to a then this will turn the object.
One example of these two situations is illustrated in the figure below. This acceleration vector has one
component along v
initial
and speeds the object up. But a has another component perpendicular to v initial
;
this turns the object.
Object
a
this part of a
speeds up the object
this part of a turns object
[10 pts] Various objects are shown below. The initial velocity vectors v
initial
as well as the acceleration
vectors a for each object are shown. Use your general rule above to determine the subsequent motion
of each of the objects (i.e., whether it is speeding up and turning, only turning, only slowing down,
etc.).
v
initial
Notice how
comparing
these vectors
requires them to
be tail-to-tail.
Object
a
v
initial
Object
a
v
initial
Object
a
v
initial
a
v
initial
Object
Object
a
v
initial
Turn these sheets in for the lab grade.
Velocity and Acceleration—4