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An automobile with 0.270 m radius tires travels 70,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
revolutions
eBook
2. –/1 points My Notes
Question Part
Points
Submissions Used
1
–/1
0/30
Total
–/1
In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 25.0 rad/s and the ball is 1.40 m from the elbow joint, what is the velocity of the ball?
m/s
eBook
3. –/2 points My Notes
A truck with 0.300 m radius tires travels at 40.0 m/s. At how many radians per second are the tires rotating? What is this in rpm?
rad/s
rpm
eBook
4. –/2 points My Notes
An ordinary workshop grindstone has a radius of 9.50 cm and rotates at 8000 rpm.
(a) Calculate the centripetal acceleration at its edge in m/s2 and convert it to multiples of g.
g
(b) What is the linear speed of a point on its edge?
m/s
eBook
5. –/4 points My Notes
(a) A 19.0 kg child is riding a playground merry-go-round that is rotating at 35.0 rpm. What centripetal force must she exert to stay on if she is 2.50 m from its center?
N
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 7.00 m from its center?
N
(c) Compare each force with her weight.
(force from part (a) / weight)
(force from part (b) / weight)
eBook
6. –/1 points My Notes
What is the ideal banking angle for a gentle turn of 1.55 km radius on a highway with a 110 km/h speed limit (about 68 mph), assuming everyone travels at the limit?
°
eBook
7. –/2 points My Notes
(a) What is the acceleration of gravity on the surface of the moon?
m/s2
(b) What is the acceleration of gravity on the surface (or outer limit) of Uranus? The mass of Uranus is 8.68 1025 kg and its radius is 2.33 107 m.
m/s2
eBook
8. –/12 points My Notes
(a) Express the following angles in radians.
30°
= rad
40°
= rad
65°
= rad
180°
= rad
(b) The following angles are in units of radians. Express them in degrees.
π/8
= °
0.70π
= °
1.8π
= °
5π
= °
(c) The following angles are in units of radians. Express them in units of revolutions.
π/8
= rev
0.70π
= rev
1.8π
= rev
5π
= rev
Physical Constants
9. –/1 points My Notes
A disk of diameter d1 rests on a table. A second disk of diameter d2 is placed with its rim touching the rim of the first disk. See the figure below. You hold the inner disk down so it does not move, and you roll the outer disk around the circumference of the first one, making sure that there is no slipping of the disk. If
d1 = 1d2,
how many revolutions does it make in one round trip?
rev
Physical Constants
10. –/2 points My Notes
Kevin decides to soup up his car by replacing the car’s wheels with ones that have 1.1 times the diameter of the original wheels. Note that the speedometer in a car is calibrated based on the tire’s diameter and on the distance the tire covers in each revolution.
(a) Will the reading of the speedometer change?
Yes No
(b) If you answered ‘Yes’ in part (a), determine the factor by which the reading of the speedometer changes. (Enter ‘NA’ if you did not answer ‘Yes’ in part (a).)
vnew
vold
=
Physical Constants
11. –/3 points My Notes
Consider a ball on a fixed-length string being whirled in a vertical circular path as shown in the diagram below.
Use the direction rosette to answer the following questions.
(a) When the ball is at location A what is the direction of the
Δv
vector?
(b) When the ball is at location B what is the direction of the
Δv
vector?
(c) When the ball is at location C what is the direction of the
Δv
vector?
Physical Constants
12. –/3 points My Notes
A rigid wheel of radius r rotates about an axis through the center and perpendicular to the plane of the wheel. Consider three points A, B, and C on the wheel, indicated by the small red circles. Location A is on the rim, locations B and C are on two different spokes of the wheel at a distance r/2 from the center. Consider the rotation of the wheel during a certain interval of time Δt.
(a) Which of the following is true regarding the angular velocity?
All three points have the same angular velocity as all three points have the same angular displacement θ in the same time interval Δt. Points B and C will have half the angular velocity of point A as they are at half the distance from the center of the wheel compared to A. Points B and C will have twice the angular velocity of point A as they are at half the distance from the center of the wheel compared to A.
(b) Which of the following is true regarding the tangential speed?
All three points have the same tangential speed as all three points have the same angular displacement θ in the same time interval Δt. Point A has a greater tangential speed as it is further away from the center of the wheel. Points B and C will have a greater tangential speed as they are closer to the center.
(c) Which of the following is true regarding centripetal acceleration? (Select all that apply.)
All three points have the same centripetal acceleration as all three points have the same angular displacement θ in the same time interval Δt. Points B and C will have half the centripetal acceleration of point A as they are at half the distance from the center of the wheel compared to A. Points B and C will have twice the centripetal acceleration of point A as they are at half the distance from the center of the wheel compared to A.
Physical Constants
13. –/2 points My Notes
You whirl a ball tied to the end of the rope in a horizontal circle at constant speed, as shown in the diagram below. Use the direction rosette to answer the following questions.
(a) What is the direction of the centripetal force acting on the ball when it is at location A?
(b) If the string breaks when the ball is at location A, in what direction will the ball move?
Physical Constants
14. –/2 points My Notes
A father fashions a swing for his kids out of a long rope that he fastens to the limb of a tall tree. As one of the kids swings from this rope that is 6.90 m long, his tangential speed at the bottom of the swing is 7.75 m/s.
(a) What is the centripetal acceleration of the kid at the bottom of the swing?
m/s2
(b) What provides the centripetal force that keeps the kid moving in an arc?
the rope the weight of the kid gravitational acceleration the height of the tree
Physical Constants
15. –/6 points My Notes
Consider a ball on a fixed-length string being whirled in a vertical circular path as shown in the diagram below.
(a) When the ball is at the bottom of the circle, what is the direction of the tension force on the ball? Use the direction rosette to answer this question.
(b) When the ball is at the bottom of the circle, what is the direction of the gravitational force on the ball? Use the direction rosette to answer this question.
(c) When the ball is at the bottom of the circle, what is the direction of the centripetal force on the ball? Use the direction rosette to answer this question.
(d) When the ball is at the bottom of the circle, what is the expression for the centripetal force on the ball? Take the upward direction as positive and the downward direction as negative when considering the sign of the forces. (Use the following as necessary: m, g and T.)
Fc =
(e) If the speed of the ball at the bottom of the circle is v, what is the expression for the centripetal force on the ball in terms of its speed v and the length L of the string? Take the upward direction as positive and the downward direction as negative when considering the sign of the forces. (Use the following as necessary: m, v and L.)
Fc =
(f) Use your answers in parts (d) and (e) to get an expression for the tension in the string in terms of the speed of the ball and the length of the string. (Use the following as necessary: m, v, g and L.)
T =
Physical Constants
16. –/2 points My Notes
Question Part
Points
Submissions Used
1
2
–/1
–/1
0/30
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Total
–/2
A heavier mass m1 and a lighter mass m2 are 18.0 cm apart and experience a gravitational force of attraction that is 8.80 10-9 N in magnitude. The two masses have a combined value of 5.65 kg. Determine the value of each individual mass.
m1 =
kg
m2 =
kg
Physical Constants
