Q: In the $$r$$-$$z$$ coordinate system for a banked curve, which equation represents the sum of forces in the $$z$$ direction?

$$\sum F_z = n \cos \theta - f_s \sin \theta - mg = 0$$

Question 1

A car is moving at a constant speed around a banked curve with no friction. Which force provides the necessary centripetal force for the car's circular motion?

Accepted Answer

The normal force component parallel to the road surface

Question 2

For a car moving slowly around a banked curve (well below the maximum speed static friction can support), which of the following best describes the direction of the net force acting on the car?

Accepted Answer

Toward the center of the curve

Question 3

A satellite is in a circular orbit just above the Earth's surface. What is the correct expression for its orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{g r}$$

Question 4

A satellite in a low-Earth orbit has a period of about 90 minutes. What is the best explanation for why this orbit is not ideal for communications satellites?

Accepted Answer

The satellite moves quickly across the sky and does not remain above one location

Question 5

What is the radius from the center of the Earth for a geostationary satellite?

Accepted Answer

$$36,000 km$$

Question 6

Which of the following equations correctly relates the net radial force to the centripetal acceleration for an object of mass $$m$$ moving in a circle of radius $$r at $$speed $$v$$?

Accepted Answer

$$F_{net} = m v^2$ / r$$

Question 7

A ball of mass $$m$$ rolls inside a horizontal pipe of radius $$r. At $$the lowest point, what is the direction of the net force on the ball?

Accepted Answer

Toward the center of the circle

Question 8

For a car on a flat road turning in a circle, which force provides the centripetal acceleration?

Accepted Answer

Static friction

Question 9

Which of the following best describes the difference between a geostationary and a geosynchronous orbit?

Accepted Answer

Geostationary orbits are always above the equator, while geosynchronous orbits can be tilted

Question 10

A ball of mass $$m$$ rolls counterclockwise inside a horizontal pipe of radius $$r. $$What is the instantaneous angular acceleration $$\alpha at $$the top of the circle, assuming only gravity acts tangentially?

Accepted Answer

$$\alpha = -g/r$$

Question 11

Which of the following is the correct expression for the period $$T of a $$satellite in a circular orbit of radius $$r$$ and speed $$v$$?

Accepted Answer

$$T = 2\pi r / v$$

Question 12

In the $$r$$-$$z$$ coordinate system for a banked curve, which equation represents the sum of forces in the $$z$$ direction?

Accepted Answer

$$\sum F_z = n \cos 	heta - f_s \sin 	heta - mg = 0$$

Question 13

A car is moving at the maximum speed that static friction can support on a banked curve. What is the direction of the static friction force?

Accepted Answer

Down the banked surface

Question 14

Which of the following best describes the net force on a satellite in a stable circular orbit around Earth?

Accepted Answer

The net force is directed radially inward toward the center of the Earth

Question 15

If the radius of a satellite's orbit is doubled, how does the required orbital speed change? (Assume a circular orbit and ignore air resistance.)

Accepted Answer

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

Question 16

A ball of mass $$m is $$rolling inside a horizontal pipe of radius $$r. At a $$certain point, the ball is speeding up. What must be true about the net force acting on the ball?

Accepted Answer

The net force has both radial and tangential components

Question 17

Which of the following is the correct relationship for angular acceleration $$\alpha in $$terms of torque $$	au$$ and moment of inertia $$I$$?

Accepted Answer

$$\alpha = 	au / I$$

Question 18

A car is moving around a flat curve of radius $$r at $$speed $$v. $$What is the maximum speed before it starts to skid, given the coefficient of static friction $$\mu_s$$?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$

Circular Dynamics and Orbits: Banked Curves, Force Analysis, and Satellite Motion

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