Question 1

During liftoff, Space Shuttle astronauts typically feel accelerations up to 1.4g, where $$g = 9.80\ \mathrm{m/s^2$}. $$What is the magnitude of the acceleration astronauts experience during liftoff in $$\mathrm{m/s^2$}$$?

Accepted Answer

$$13.7\ \mathrm{m/s^2$}$$

Question 2

In astronaut training, astronauts ride in a device where they experience a centripetal acceleration of $$1.4g in a $$circle of radius $$10.0\ \mathrm{m}. $$What is the required rotation rate in revolutions per second?

Accepted Answer

$$0.59\ \mathrm{rev/s}$$

Question 3

Young David swings a sling of length $$0.600\ \mathrm{m} at a $$rate of $$0.840\ \mathrm{rev/s}. $$What is the speed of the stone?

Accepted Answer

$$3.17\ \mathrm{m/s}$$

Question 4

If David increases the length of the sling to $$0.900\ \mathrm{m}$$ and can revolve the sling $$0.600$$ times per second, what is the speed of the stone?

Accepted Answer

$$3.39\ \mathrm{m/s}$$

Question 5

A student attaches a ball to the end of a string $$0.600\ \mathrm{m} in $$length and swings the ball in a vertical circle. The speed of the ball is $$4.00\ \mathrm{m/s} at $$its highest point and $$6.00\ \mathrm{m/s} at $$its lowest point. What is the centripetal acceleration at the lowest point?

Accepted Answer

$$36.0\ \mathrm{m/s^2$}$$

Question 6

A train slows down as it rounds a sharp horizontal curve, slowing from $$90.0\ \mathrm{km/h} to$$ $$50.0\ \mathrm{km/h} in$$ $$15.0\ \mathrm{s}. $$The radius of the curve is $$150\ \mathrm{m}. $$What is the magnitude of the total acceleration at the moment the train speed reaches $$50.0\ \mathrm{km/h}$$?

Accepted Answer

$$1.39\ \mathrm{m/s^2$}$$

Question 7

An automobile whose speed is increasing at a rate of $$0.600\ \mathrm{m/s^2$}$$ travels along a circular road of radius $$20.0\ \mathrm{m}. $$When the instantaneous speed of the automobile is $$4.00\ \mathrm{m/s}$$, what is the magnitude of the radial (centripetal) acceleration component?

Accepted Answer

$$0.800\ \mathrm{m/s^2$}$$

Question 8

For the automobile in the previous question, what is the magnitude of the total acceleration?

Accepted Answer

$$1.00\ \mathrm{m/s^2$}$$

Question 9

A ball is swung in a vertical circle of radius $$0.600\ \mathrm{m}. At $$its highest point, the speed is $$4.00\ \mathrm{m/s}. $$What is the centripetal acceleration at the highest point?

Accepted Answer

$$26.7\ \mathrm{m/s^2$}$$

Question 10

A train rounds a curve of radius $$150\ \mathrm{m} at a $$constant speed of $$50.0\ \mathrm{km/h}. $$What is the centripetal acceleration?

Accepted Answer

$$1.29\ \mathrm{m/s^2$}$$

Question 11

An astronaut is fastened securely at the end of a mechanical arm that turns at a constant rate in a horizontal circle of radius $$10.0\ \mathrm{m}. $$What is the required speed to achieve a centripetal acceleration of $$1.4g$$?

Accepted Answer

$$11.8\ \mathrm{m/s}$$

Question 12

A car travels around a circular track of radius $$20.0\ \mathrm{m} at a $$speed of $$4.00\ \mathrm{m/s}. $$What is the direction of the radial acceleration component?

Accepted Answer

Toward the center of the circle

Question 13

A train slows down from $$90.0\ \mathrm{km/h} to$$ $$50.0\ \mathrm{km/h} in$$ $$15.0\ \mathrm{s}$$ while rounding a curve of radius $$150\ \mathrm{m}. $$What is the tangential acceleration?

Accepted Answer

$$-0.74\ \mathrm{m/s^2$}$$

Question 14

A ball is swung in a vertical circle. At its lowest point, the tension in the string must be greatest because:

Accepted Answer

It must support both the weight of the ball and provide the centripetal force

Question 15

An astronaut in a centrifuge experiences a centripetal acceleration of $$1.4g. If $$the radius of the centrifuge is doubled, what happens to the required angular velocity to maintain the same acceleration?

Accepted Answer

It decreases by a factor of $$\sqrt{2}$$

Question 16

A car moves in a circle of radius $$20.0\ \mathrm{m}$$ with a speed of $$4.00\ \mathrm{m/s}$$ and a tangential acceleration of $$0.600\ \mathrm{m/s^2$}. $$What is the angle between the total acceleration vector and the radial direction?

Accepted Answer

$$36.9^\circ$$

Question 17

If the centripetal acceleration is given by $$a_c = \frac{v^2$}{r}$$, what happens to $$a_c if $$the speed is doubled?

Accepted Answer

It increases by a factor of 4

Question 18

A ball is swung in a vertical circle. At its highest point, what is the minimum speed required so that the string remains taut?

Accepted Answer

$$\sqrt{g r}$$

Centripetal Acceleration, Circular Motion, and Related Applications

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