Q: A projectile is launched with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the formula for the range $$R of $$the projectile?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Question 1

A car of mass $$m is $$making a left turn around a curve of radius $$r on a $$level (unbanked) road. If the coefficient of static friction between the tires and the road is $$\mu_s$$, what is the maximum speed $$v_{max}$$ the car can have without sliding?

Accepted Answer

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

Question 2

A hockey puck is tied by a string to a stake in the ice and swung in a circle. What force is responsible for producing the centripetal acceleration of the puck?

Accepted Answer

Tension in the string

Question 3

A car moves around a circular track at constant speed $$v. If $$the speed suddenly doubles, by what factor does the centripetal acceleration change?

Accepted Answer

It increases by a factor of 4

Question 4

For a particle in uniform circular motion of radius $$r$$ and angular speed $$\omega$$, what is the magnitude of the centripetal acceleration?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 5

A projectile is launched with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the formula for the range $$R of $$the projectile?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 6

A satellite orbits Earth in a circular path. What provides the centripetal force required for its motion?

Accepted Answer

The gravitational force

Question 7

On a frictionless road, a car attempts to turn a corner. What happens to the car?

Accepted Answer

It continues in a straight line tangent to the curve

Question 8

A car of mass $$m is $$moving at speed $$v$$ around a banked curve of radius $$r$$ and banking angle $$	heta. If $$there is no friction, what is the exact speed $$v at $$which the car can take the curve without sliding?

Accepted Answer

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

Question 9

Which of the following statements about centripetal force is correct?

Accepted Answer

Centripetal force is not a new type of force, but the name given to the net force pointing toward the center of circular motion

Question 10

A car is moving too slowly around a banked curve. What direction must the static friction force point to prevent the car from sliding down the incline?

Accepted Answer

Uphill, parallel to the surface

Question 11

A ball is swung in a vertical circle at constant speed. At the top of the circle, what is the direction of the net force acting on the ball?

Accepted Answer

Downward, toward the center of the circle

Question 12

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What launch angle gives the maximum range?

Accepted Answer

$$	heta = 45^\circ$$

Question 13

Which force allows a car to turn a corner on a level road?

Accepted Answer

Static friction between the tires and the road

Question 14

A particle moves in a circle of radius $$r at $$constant speed $$v. $$What is the direction of its acceleration?

Accepted Answer

Toward the center of the circle

Question 15

A roller coaster car of mass $$m$$ moves through a vertical loop of radius $$r. $$What is the minimum speed $$v_{min} at $$the top of the loop to maintain contact with the track?

Accepted Answer

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

Question 16

A projectile is subject to air resistance. How does this affect its trajectory compared to the ideal case?

Accepted Answer

The range and maximum height are both reduced

Question 17

A car of mass $$m is $$moving at speed $$v$$ around a curve of radius $$r. $$What is the required centripetal force?

Accepted Answer

$$F_c = \frac{m v^2$}{r}$$

Question 18

A car is moving too fast around a banked curve. What direction must the static friction force point to prevent the car from sliding up the incline?

Accepted Answer

Downhill, parallel to the surface

Question 19

Which of the following is true about the acceleration of a particle moving in a circle at constant speed?

Accepted Answer

It has only a radial (centripetal) component

Question 20

A ball is swung in a horizontal circle at constant speed. If the string breaks, what path will the ball follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point of release

Dynamics II: Motion in a Plane – Newton’s Laws in Two Dimensions

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