Q: A car of mass $$m$$ travels around a flat, unbanked curve of radius $$r. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed the car can have without sliding?

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

Q: A 600-kg car is going around a banked curve of radius $$110\ \mathrm{m} at$$ $$24.5\ \mathrm{m/s}. $$What banking angle $$\theta$$ allows the car to make the turn without friction?

$$\theta = \arctan\left(\frac{v^2$}{r g}\right) = 29.1^\circ$$

Q: A roller coaster car of mass $$m$$ traverses a vertical loop of radius $$r. $$What is the minimum speed at the top of the loop so that the car remains in contact with the track?

$$v_{\text{min}} = \sqrt{g r}$$

Q: A 110 kg sled and rider go over a rise shaped as a circle of radius $$4.1\ \mathrm{m} at$$ $$2.7\ \mathrm{m/s}. If $$the coefficient of kinetic friction is $$0.10$$, what is the friction force exerted by the snow?

$$f_k = \mu_k m g = 0.10 \times 110 \times 9.8 = 108\ \mathrm{N}$$

Question 1

A 30 kg weather rocket is launched vertically upward with a thrust of 1500 N. A constant horizontal wind exerts a 20 N force on the rocket. Neglecting air resistance, what is the rocket's horizontal deflection when it has reached a height of 1000 m? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$17\ \mathrm{m}$$

Question 2

A car of mass $$m$$ travels around a flat, unbanked curve of radius $$r. If $$the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed the car can have without sliding?

Accepted Answer

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

Question 3

A 600-kg car is going around a banked curve of radius $$110\ \mathrm{m} at$$ $$24.5\ \mathrm{m/s}. $$What banking angle $$	heta$$ allows the car to make the turn without friction?

Accepted Answer

$$	heta = \arctan\left(\frac{v^2$}{r g}ight) = 29.1^\circ$$

Question 4

A roller coaster car of mass $$m$$ traverses a vertical loop of radius $$r. $$What is the minimum speed at the top of the loop so that the car remains in contact with the track?

Accepted Answer

$$v_{	ext{min}} = \sqrt{g r}$$

Question 5

A Ferris wheel has a diameter of $$10\ \mathrm{m}$$ and makes one revolution every $$8.0\ \mathrm{s}. A $$person weighing $$670\ \mathrm{N}$$ sits at the rim. What is the apparent weight (normal force) on the person at the highest point?

Accepted Answer

$$N = 670\ \mathrm{N} - m \frac{v^2$}{r}$$

Question 6

A projectile is launched at speed $$v_0$$ and angle $$	heta$$ above the horizontal. Neglecting air resistance, what launch angle maximizes the range?

Accepted Answer

$$45^\circ$$

Question 7

When air resistance (drag) is included, the launch angle that maximizes the range of a projectile is:

Accepted Answer

Less than $$45^\circ$$

Question 8

A toy car moves around a circular track at constant speed. If its speed doubles, by what factor does its centripetal acceleration change?

Accepted Answer

It increases by a factor of $$4$$

Question 9

A satellite orbits Earth in a circular orbit of radius $$r. $$What is the required speed for the satellite to remain in orbit, neglecting air resistance?

Accepted Answer

$$v = \sqrt{\frac{G M}{r}}$$

Question 10

A car coasts over the top of a hill with speed $$v. $$The hill has radius $$r. $$What is the normal force on the car at the top of the hill?

Accepted Answer

$$N = m g - m \frac{v^2$}{r}$$

Question 11

Which of the following statements about the centrifugal force is correct?

Accepted Answer

It is a fictitious force that appears in non-inertial reference frames.

Question 12

A 110 kg sled and rider go over a rise shaped as a circle of radius $$4.1\ \mathrm{m} at$$ $$2.7\ \mathrm{m/s}. If $$the coefficient of kinetic friction is $$0.10$$, what is the friction force exerted by the snow?

Accepted Answer

$$f_k = \mu_k m g = 0.10 	imes 110 	imes 9.8 = 108\ \mathrm{N}$$

Question 13

Which force provides the centripetal acceleration for a car turning on a flat road?

Accepted Answer

Static friction between the tires and the road

Question 14

In uniform circular motion, what is the direction of the net force acting on the object?

Accepted Answer

Toward the center of the circle

Question 15

A projectile is launched horizontally from a tower on a spherical, airless planet. As the launch speed increases, what happens to the trajectory?

Accepted Answer

It becomes more curved and eventually matches the curvature of the planet, resulting in an orbit.

Question 16

Which coordinate system is most convenient for analyzing circular motion?

Accepted Answer

rtz-coordinates (radial, tangential, perpendicular)

Question 17

A hockey puck is tied to a stake and swung in a circle on frictionless ice. What force is responsible for the puck's centripetal acceleration?

Accepted Answer

Tension in the string

Question 18

In nonuniform circular motion, which of the following is true?

Accepted Answer

There are both radial and tangential components of acceleration.

Question 19

A car travels around a banked curve of radius $$r at $$the exact speed for which no friction is required. What provides the necessary centripetal force?

Accepted Answer

The radial component of the normal force

Question 20

Why do astronauts in the International Space Station feel weightless?

Accepted Answer

They are in continuous free fall around Earth.

Dynamics II: Motion in a Plane – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards