Q: A civil engineer wants to design a banked curve so that a car can round it without friction at speed $$v$$ and radius $$r. $$What angle $$\theta$$ should the curve be banked at?

$$\tan \theta = \frac{v^2$}{r g}$$

Question 1

Which scientist is credited with the first measurement of the universal gravitational constant, $$G$$?

Accepted Answer

Henry Cavendish

Question 2

An object moves in a circle of radius $$r at $$constant speed $$v. $$What is the correct expression for the centripetal acceleration $$a_c$$?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 3

A car of mass $$m$$ travels around a flat circular turn of radius $$r at $$speed $$v. $$What minimum coefficient of static friction $$\mu_s is $$required to prevent the car from sliding?

Accepted Answer

$$\mu_s = \frac{v^2$}{r g}$$

Question 4

Which of the following best describes the force that acts as the centripetal force for a coin sitting on a rotating turntable?

Accepted Answer

Static friction

Question 5

A satellite orbits Earth at a distance $$r$$ from the center of the Earth. What is the correct expression for its orbital speed $$v_{orbit}$$?

Accepted Answer

$$v_{orbit} = \sqrt{g r}$$

Question 6

According to Newton’s law of universal gravitation, what happens to the gravitational force between two masses if the distance between them is doubled?

Accepted Answer

It becomes one-fourth as great

Question 7

Which of the following is NOT a correct statement about centripetal force?

Accepted Answer

It is a new fundamental force of nature

Question 8

A projectile is launched horizontally from a high altitude. As its speed increases, what happens to its trajectory relative to the curvature of the Earth?

Accepted Answer

It eventually matches the curvature of the Earth and enters orbit

Question 9

What is the escape speed from the surface of the Earth, and what does it depend on?

Accepted Answer

11.2 km/s; independent of the mass of the object

Question 10

Kepler’s First Law states that:

Accepted Answer

Planets move in elliptical orbits with the Sun at one focus

Question 11

A planet moves fastest in its orbit when it is:

Accepted Answer

At perihelion

Question 12

Which of the following best describes weightlessness experienced by astronauts in orbit?

Accepted Answer

Astronauts are in continuous free fall around the Earth

Question 13

The gravitational force between two objects of masses $$m_1$$ and $$m_2$$ separated by distance $$r is $$given by:

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 14

If the radius of the Earth were doubled but its mass remained the same, what would happen to the acceleration due to gravity at the surface?

Accepted Answer

It would become one-fourth as great

Question 15

Kepler’s Third Law can be written as $$T^2$$ \propto $$a^3. $$What does $$a$$ represent in this equation?

Accepted Answer

The semi-major axis of the orbit

Question 16

Which of the following is a correct expression for the gravitational potential energy of a mass $$m at a $$distance $$r$$ from the center of the Earth (mass $$M_E$$)?

Accepted Answer

$$PE = -\frac{G M_E m}{r}$$

Question 17

A civil engineer wants to design a banked curve so that a car can round it without friction at speed $$v$$ and radius $$r. $$What angle $$	heta$$ should the curve be banked at?

Accepted Answer

$$	an 	heta = \frac{v^2$}{r g}$$

Question 18

Which of the following best explains why a centrifuge can separate components of a liquid with different densities?

Accepted Answer

It creates a strong centripetal acceleration, causing denser components to move outward due to inertia

Question 19

Which of the following orbits has the highest eccentricity?

Accepted Answer

Comet Halley's orbit

Circular Motion, Orbits, and Gravity: Study Notes

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