Q: A 5.0 kg cannonball is fired horizontally at 64 m/s from a 16-m-high cliff. A strong tailwind exerts a constant 12 N horizontal force in the direction the cannonball is traveling. What is the extra horizontal distance the cannonball travels due to the wind? (Take $$g = 9.8 m/s$^2.)$$

$$d = \frac{F_{\text{wind}} y_0$}{mg}$$

Q: A small metal cylinder rests on a circular turntable rotating at constant speed. The mass is 0.20 kg, the coefficient of static friction is 0.080, and the cylinder is 0.15 m from the center. What is the maximum speed $$v_{\text{max}}$$ the cylinder can move without slipping?

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

Q: A car drives over the top of a hill with radius 40 m. What is the maximum speed the car can have without flying off the road at the top?

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

Q: Suppose you swing a ball of mass $$m in a $$vertical circle on a string of length $$L. $$What is the minimum angular velocity $$\omega_{\text{min}}$$ required for the ball to complete the circle without the string going slack at the top?

$$\omega_{\text{min}} = \sqrt{\frac{g}{L}}$$

Q: A cyclist competes in a one-lap race around a flat, circular course of radius 140 m, starting from rest and speeding up at a constant rate, covering the course in 60 s. What is the magnitude of the net force acting on the bicycle as it crosses the finish line if the mass is 76 kg?

$$F_{\text{net}} = m \sqrt{a_t^2$ + a_r^2$}$$

Question 1

A 5.0 kg cannonball is fired horizontally at 64 m/s from a 16-m-high cliff. A strong tailwind exerts a constant 12 N horizontal force in the direction the cannonball is traveling. What is the extra horizontal distance the cannonball travels due to the wind? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$d = \frac{F_{	ext{wind}} y_0$}{mg}$$

Question 2

A model rocket of mass 0.400 kg is on a cart rolling to the right at 4.0 m/s. The rocket engine exerts an 8.0 N vertical thrust. If the rocket must pass through a hoop 20 m above the launch point, what is the vertical acceleration of the rocket?

Accepted Answer

$$a_y = \frac{F_{R} - mg}{m}$$

Question 3

A 240 g block on a 58.0-cm-long string swings in a circle on a horizontal, frictionless table at 75.0 rpm. What is the speed of the block?

Accepted Answer

$$v = r \omega$$

Question 4

What is the tension in the string for the block described above?

Accepted Answer

$$T = \frac{mv^2$}{r}$$

Question 5

A space station is constructed as a 1000-m diameter cylinder that rotates about its axis. What rotation period will provide 'normal' gravity ($$g = 9.8 m/s$^2$$)?

Accepted Answer

$$T = 2\pi \sqrt{\frac{r}{g}}$$

Question 6

A communications satellite is placed in a geosynchronous orbit. What is the period of a satellite in this orbit?

Accepted Answer

$$T = 24.0 hr$$

Question 7

What is the weight of a 2000 kg satellite in a geosynchronous orbit where $$g = 0.223 m/s$^2$$?

Accepted Answer

$$W = mg = 446 N$$

Question 8

A small metal cylinder rests on a circular turntable rotating at constant speed. The mass is 0.20 kg, the coefficient of static friction is 0.080, and the cylinder is 0.15 m from the center. What is the maximum speed $$v_{	ext{max}}$$ the cylinder can move without slipping?

Accepted Answer

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

Question 9

A car drives over the top of a hill with radius 40 m. What is the maximum speed the car can have without flying off the road at the top?

Accepted Answer

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

Question 10

A new car is tested on a 200-m diameter track. If the car speeds up at a steady 1.3 m/s$$^2$$, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Accepted Answer

$$\Delta t = \sqrt{\frac{r}{a_t}}$$

Question 11

Suppose you swing a ball of mass $$m in a $$vertical circle on a string of length $$L. $$What is the minimum angular velocity $$\omega_{	ext{min}}$$ required for the ball to complete the circle without the string going slack at the top?

Accepted Answer

$$\omega_{	ext{min}} = \sqrt{\frac{g}{L}}$$

Question 12

A cyclist competes in a one-lap race around a flat, circular course of radius 140 m, starting from rest and speeding up at a constant rate, covering the course in 60 s. What is the magnitude of the net force acting on the bicycle as it crosses the finish line if the mass is 76 kg?

Accepted Answer

$$F_{	ext{net}} = m \sqrt{a_t^2$ + a_r^2$}$$

Question 13

In circular motion, what force provides the centripetal acceleration for a small metal cylinder on a rotating turntable?

Accepted Answer

Static friction

Question 14

A rider stands inside an 18.0-m diameter rotating ring (The Roundup). If the ring rotates once every 5.40 s and the rider's mass is 59.0 kg, what is the force with which the ring pushes on her at the top of the ride?

Accepted Answer

$$F = m (\$$omega^2$$ r - g)$$

Question 15

A golfer swings her club, and halfway through the swing, when the club is parallel to the ground, where does the acceleration vector of the club head point?

Accepted Answer

Approximately toward the golfer's feet

Question 16

A small metal cylinder rests on a turntable rotating at constant speed. If the cylinder is moved to a new location at $$R/2$$ from the center, what happens to its speed and acceleration?

Accepted Answer

The speed of the cylinder has decreased, but the magnitude of the acceleration has increased.

Question 17

For a mass $$m$$ moving in a circle of radius $$r$$ with speed $$v$$, what is the magnitude of the centripetal acceleration?

Accepted Answer

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

Question 18

A cyclist moves in a circle at increasing speed. Which force provides both tangential and radial acceleration?

Accepted Answer

Static friction

Analyzing Forces on a Mass in Uniform Circular Motion

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