Relation between magnitude of acceleration, speed and turning radius. Parts of two ovals are shown. Two cars travel counterclockwise around the two paths at the same constant speed. The distance and time intervals between the two points on each path are the same. Draw the change in velocity vector between the points A and C in each case. a. b. Does the magnitude of the acceleration at point B increase or decrease when we decrease the turning radius? C. VA vc B B C Assume the cars drive around the same track at a larger but still constant speed. If we repeat the steps above with larger velocity vectors, would the magnitude of the acceleration at B increase or decrease?

Physics for Scientists and Engineers
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Chapter6: Circular Motion And Other Applications Of Newton's Laws
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Physics 211 - Module 1 Hands On Activities Packet 2
Activity 1.17 - Motion on a Curve
Acceleration for an object turning at constant speed.
1. Relation between direction of acceleration and velocity while turning at constant speed.
a.
The path for a car driving clockwise around an oval at
constant speed is shown. Draw and label vectors VA, VB
and showing the velocity vectors at the three points
A, B and C.
b. In the box, draw a diagram showing the relation
between A, C and Av=c-VA.
C.
What is the relation between the direction of Av
between A and C and the direction of the average
acceleration at between point A and C?
AV
рад
U
+
d. The acceleration at B is approximately equal to the average acceleration between points A and C. Draw and label
the acceleration vector at point B. What is the angle between the velocity and acceleration vectors at point B?
90°
C.
This relation between the directions of the velocity and acceleration is true in whenever an object is turning at
constant speed.
e. Draw vectors showing the direction of the acceleration at points A and C.
2. Relation between magnitude of acceleration, speed and turning radius.
a. Parts of two ovals are shown. Two cars
travel counterclockwise around the two
paths at the same constant speed. The
distance and time intervals between the
two points on each path are the same.
Draw the change in velocity vector between
the points A and C in each case.
b. Does the magnitude of the acceleration at point
B increase or decrease when we decrease the
turning radius?
Student Add Name Here
A
VA
B
В
Assume the cars drive around the same track at a larger but still constant speed. If we repeat the steps above
with larger velocity vectors, would the magnitude of the acceleration at B increase or decrease?
Physics 211 - Module 1 Hands On Activities Packet 2
d. The car travels at constant speed clockwise around the
path shown. Draw acceleration vectors at the dots.
Draw longer vectors where the acceleration is larger.
Write a where the acceleration zero.
For an object moving at constant speed the acceleration
is perpendicular to the velocity and into the turn. This is
called the centripetal (center-seeking) acceleration with
magnitude acent=v²/r where v is the speed and r is
the radius of curvature of the turn.
Object moving at increasing speed.
a.
Assume the car driving clockwise around the oval increases
its speed so it is traveling faster at point C than at point A.
b. In the box, draw a diagram showing the relation between
VA, Vc and Av = vc - VA
c. What is the angle between the velocity vector at point B
and the acceleration at point B? Is the angle larger smaller
or equal to 90°?
Student Add Name Here
a
d. Now assume that the car slows down as it goes from point A to point C. What is the angle between the velocity
vector at point B and the acceleration at point B in this case? Is the angle larger smaller or equal to 90°
CONCLUSION: When an object turns there is always a centripetal acceleration into the turn. If the object also
changes speed, there is an additional component parallel or anti-parallel to the velocity called the tangential
acceleration of magnitude atan = |dv/dt |.
B
Transcribed Image Text:Physics 211 - Module 1 Hands On Activities Packet 2 Activity 1.17 - Motion on a Curve Acceleration for an object turning at constant speed. 1. Relation between direction of acceleration and velocity while turning at constant speed. a. The path for a car driving clockwise around an oval at constant speed is shown. Draw and label vectors VA, VB and showing the velocity vectors at the three points A, B and C. b. In the box, draw a diagram showing the relation between A, C and Av=c-VA. C. What is the relation between the direction of Av between A and C and the direction of the average acceleration at between point A and C? AV рад U + d. The acceleration at B is approximately equal to the average acceleration between points A and C. Draw and label the acceleration vector at point B. What is the angle between the velocity and acceleration vectors at point B? 90° C. This relation between the directions of the velocity and acceleration is true in whenever an object is turning at constant speed. e. Draw vectors showing the direction of the acceleration at points A and C. 2. Relation between magnitude of acceleration, speed and turning radius. a. Parts of two ovals are shown. Two cars travel counterclockwise around the two paths at the same constant speed. The distance and time intervals between the two points on each path are the same. Draw the change in velocity vector between the points A and C in each case. b. Does the magnitude of the acceleration at point B increase or decrease when we decrease the turning radius? Student Add Name Here A VA B В Assume the cars drive around the same track at a larger but still constant speed. If we repeat the steps above with larger velocity vectors, would the magnitude of the acceleration at B increase or decrease? Physics 211 - Module 1 Hands On Activities Packet 2 d. The car travels at constant speed clockwise around the path shown. Draw acceleration vectors at the dots. Draw longer vectors where the acceleration is larger. Write a where the acceleration zero. For an object moving at constant speed the acceleration is perpendicular to the velocity and into the turn. This is called the centripetal (center-seeking) acceleration with magnitude acent=v²/r where v is the speed and r is the radius of curvature of the turn. Object moving at increasing speed. a. Assume the car driving clockwise around the oval increases its speed so it is traveling faster at point C than at point A. b. In the box, draw a diagram showing the relation between VA, Vc and Av = vc - VA c. What is the angle between the velocity vector at point B and the acceleration at point B? Is the angle larger smaller or equal to 90°? Student Add Name Here a d. Now assume that the car slows down as it goes from point A to point C. What is the angle between the velocity vector at point B and the acceleration at point B in this case? Is the angle larger smaller or equal to 90° CONCLUSION: When an object turns there is always a centripetal acceleration into the turn. If the object also changes speed, there is an additional component parallel or anti-parallel to the velocity called the tangential acceleration of magnitude atan = |dv/dt |. B
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