Question 1

Which of the following best describes the 'flat-earth approximation' in projectile motion?

Accepted Answer

Gravity acts vertically downward and the ground is considered flat.

Question 2

A projectile is launched horizontally from a tower of height $$h on a $$spherical planet. If its initial speed $$v_0 is $$very small, what type of trajectory will it follow?

Accepted Answer

It will follow a parabolic trajectory and fall to the ground.

Question 3

As the initial speed $$v_0 of a $$horizontally launched projectile increases, what happens to its range?

Accepted Answer

The range increases as the ground curves away from the projectile.

Question 4

At what point does a projectile launched horizontally from a planet's surface enter an orbit?

Accepted Answer

When its trajectory and the curve of the planet are parallel.

Question 5

In the flat-earth approximation, what is the direction of the gravitational force on an object of mass $$m$$?

Accepted Answer

$$F_G = mg$$ vertically downward

Question 6

For a real spherical planet, what is the direction of the gravitational force on an object at the surface?

Accepted Answer

$$F_G = mg$$ toward the center of the planet

Question 7

What is the required speed for a circular orbit near a planet’s surface, neglecting air resistance?

Accepted Answer

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

Question 8

A satellite in low-earth orbit is said to be in 'free fall.' What does this mean?

Accepted Answer

It is falling under the influence only of gravity, following a curved path around Earth.

Question 9

Why do astronauts feel weightless while orbiting Earth in the International Space Station?

Accepted Answer

They are in continuous free fall, accelerating toward Earth at the same rate as the station.

Question 10

Which of the following is true about the 'centrifugal force' experienced in a rotating reference frame?

Accepted Answer

It is a fictitious force that appears to act outward in a non-inertial (rotating) frame.

Question 11

A car makes a left turn. From the perspective of an observer inside the car, what force do they feel?

Accepted Answer

A fictitious centrifugal force pushing them toward the outside of the curve.

Question 12

An object in a low circular orbit has acceleration $$a = \frac{F_{net}}{m} = g$$ toward the center. If the object moves in a circle of radius $$r at $$speed $$v_{orbit}$$, what is the centripetal acceleration?

Accepted Answer

$$a_r = \frac{v_{orbit}^2}{r}$$

Question 13

A roller coaster car is at the bottom of a vertical loop. What is the direction of the net force acting on the car?

Accepted Answer

Upward, toward the center of the loop.

Question 14

At the top of a roller coaster loop, the normal force from the track on the car is:

Accepted Answer

Directed downward, toward the center of the loop.

Question 15

What is the critical speed $$v_{critical} at $$the top of a roller coaster loop of radius $$r so $$that the car does not fall off?

Accepted Answer

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

Question 16

A physics textbook swings as a pendulum. At the bottom of its swing, moving to the right, what is the direction of the net force?

Accepted Answer

Upward, toward the center of the circular path.

Question 17

A ball rolls counterclockwise inside a horizontal pipe. At the highest point, moving down, what is the direction of the net force on the ball?

Accepted Answer

Downward, toward the center of the circle.

Question 18

Which equation gives the period $$T of a $$low-Earth-orbit satellite, assuming $$r is $$the radius of the Earth?

Accepted Answer

$$T = \frac{2 \pi r}{v_{orbit}}$$

Question 19

On a rotating Earth, the free-fall acceleration measured by a spring scale at the equator is:

Accepted Answer

$$g = \frac{GM}{R^2$} - \$$omega^2$$ R$$

Circular Orbits and Projectile Motion: Study Notes for University Physics

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