Question 1

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?
A) 29.1°
B) 13.5°
C) 33.8°
D) 56.2°
E) 60.9°

Accepted Answer

A

Question 2

A Ferris wheel has diameter of 10 m and makes one revolution in 8.0 seconds. A person weighing 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (that is, the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?

Accepted Answer

460 N

Question 3

Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station 390 m diameter rotating about its central axis. Astronauts walk on the inside surface of the space station. What rotation period will provide "normal" gravity?
A) 28 s
B) 40 s
C) 6.3 s
D) 4.4 s

Accepted Answer

To provide "normal" gravity, the centripetal acceleration at the surface must equal the acceleration due to gravity on Earth ($g = 9.8 \, \text{m/s}^2$). The formula for centripetal acceleration is $a = \frac{v^2}{r}$, where $v$ is the linear velocity and $r$ is the radius of the circle. Since $v = \frac{2\pi r}{T}$, where $T$ is the period, we can substitute $v$ into the acceleration formula to get $a = \frac{4\pi^2 r}{T^2}$. Setting $a = g$ and solving for $T$ gives $T = \sqrt{\frac{4\pi^2 r}{g}}$. The radius $r$ is half the diameter, so $r = 195 \, \text{m}$. Plugging in the values gives $T = \sqrt{\frac{4\pi^2 \times 195}{9.8}} \approx 28 \, \text{s}$.

Question 4

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?
A) 9.25 m/s
B) 23.6 m/s
C) 34.3 m/s
D) 35.0 m/s
E) 18.5 m/s

Accepted Answer

The car will begin to skid sideways when the centripetal force required to keep the car moving in a circle exceeds the maximum static friction force. The maximum static friction force can be calculated using $f_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. For a car of mass $m$ on a horizontal surface, $N = mg$, where $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$). The centripetal force required for circular motion is given by $F_c = \frac{mv^2}{r}$, where $v$ is the velocity of the car and $r$ is the radius of the curve. Setting the maximum static friction force equal to the required centripetal force gives $\mu_s mg = \frac{mv^2}{r}$. Solving for $v$ gives $v = \sqrt{\mu_s g r}$. Substituting $\mu_s = 0.350$, $g = 9.8 \, \text{m/s}^2$, and $r = 100 \, \text{m}$ gives $v = \sqrt{0.350 \times 9.8 \times 100} = \sqrt{343} \approx 18.5 \, \text{m/s}$.

Question 5

Engineers are designing a curved section of a highway. If the radius of curvature of the curve is  at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?
A) 23.9°
B) 16.7°
C) 21.0°
D) 26.1°

Accepted Answer

The answer of Engineers are designing a curved section of...

Question 6

A person on a sled coasts down a hill and then goes over a slight rise with speed 2.7 m/s. The top of this rise can be modeled as a circle of radius 4.1 m. The sled and occupant have a combined mass of 110 kg. If the coefficient of kinetic friction between the snow and the sled is 0.10, what friction force is exerted on the sled by the snow as the sled goes over the top of the rise?

Accepted Answer

The answer of A person on a sled coasts down...

Question 7

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?
A) 29.6 m/s
B) 33.1 m/s
C) 24.8 m/s
D) 42.0 m/s
E) 37.9 m/s

Accepted Answer

The answer of A car enters a 300-m radius horizontal...

Question 8

A ball of mass 5.0 kg is suspended by two wires from a horizontal arm that is attached to a vertical shaft, as shown in the figure. The shaft is in uniform rotation about its axis. The rate of rotation is adjusted until the tensions in the two wires are EQUAL. At that speed, the radial acceleration of the ball is closest to A) 4.9 m/s². B) 5.9 m/s². C) 6.9 m/s². D) 7.9 m/s². E) 9.9 m/s².

Accepted Answer

The answer of A ball of mass 5.0 kg is...

Question 9

A car drives over a hilltop that has a radius of curvature 0.120 km at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?
A) 45.5 m/s
B) 41.8 m/s
C) 34.3 m/s
D) 22.2 m/s
E) 27.6 m/s

Accepted Answer

For the tires to just barely lose contact with the road at the top of the hill, the centripetal force must equal the gravitational force acting on the car. The formula for centripetal force is $F_c = \frac{mv^2}{r}$, where $m$ is the mass of the car, $v$ is the velocity, and $r$ is the radius of curvature. The gravitational force is $F_g = mg$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Setting these two forces equal gives $\frac{mv^2}{r} = mg$, which simplifies to $v^2 = rg$. Plugging in $r = 0.120 km = 120 m$ and $g = 9.8 m/s^2$, we find $v = \sqrt{120m \times 9.8 m/s^2} = \sqrt{1176} m/s \approx 34.3 m/s$.

Question 10

A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.
A) 11.4 m/s
B) 12.5 m/s
C) 10.1 m/s
D) 14.9 m/s

Accepted Answer

The answer of A new roller coaster contains a loop-the-loop...

Question 11

Suppose a highway curve is properly banked to eliminate friction for a speed of 45 mph. If your tires were bald and you wanted to avoid sliding on the road, you would have to drive
A) somewhat below 45 mph.
B) somewhat above 45 mph.
C) at exactly 45 mph.

Accepted Answer

The answer of Suppose a highway curve is properly banked...

Question 12

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out because an outward force balances the pull of gravity on the water.

Accepted Answer

At the highest point, the water does not spill out because the centripetal force required to keep it in circular motion is provided by the force of gravity acting on the water, not an outward force.

Question 13

The figure shows two wires that are tied to a 710 g mass that revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in the upper wire? 
A) 34 N
B) 20 N
C) 27 N
D) 41 N

Accepted Answer

The answer of The figure shows two wires that are...

Question 14

A roadway for stunt drivers is designed for racecars moving at a speed of 40 m/s. A curved section of the roadway is a circular arc of 230 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?
A) 35°
B) 37°
C) 33°
D) 31°
E) 29°

Accepted Answer

The answer of A roadway for stunt drivers is designed...

Question 15

The figure shows two wires tied to a 3.3 kg sphere that revolves in a horizontal circle at constant speed. At this particular speed the tension is the SAME in both wires. What is the tension? 
A) 24 N
B) 32 N
C) 44 N
D) 22 N

Accepted Answer

The answer of The figure shows two wires tied to...

Question 16

A 600-kg car traveling at 24.5 m/s is going around a curve having a radius of 120 m that is banked at an angle of 20°.
(a) Is the curve properly banked for the car's speed?
(b) What is the minimum coefficient of static friction required between the road and the car's tires so the car does not skid?

Accepted Answer

The answer of A 600-kg car traveling at 24.5 m/s...

Question 17

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m. What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?
A) 1.23
B) 0.816
C) 0.736
D) 0.952
E) 0.662

Accepted Answer

The centripetal force required to keep the car moving in a circle of radius 200 m at a speed of 40.0 m/s is given by:

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

where m is the mass of the car and r is the radius of the curve.

Assuming that the car is not sliding, the friction force between the tires and the road provides the centripetal force. Thus, we can write:

$f = \mu_s N$

where f is the friction force, $\mu_s$ is the coefficient of static friction, and N is the normal force (equal to the weight of the car).

The maximum speed at which the car can travel around the curve without sliding is when the friction force is equal to the maximum possible value, given by $\mu_s N$. Thus, we can set $F_c = \mu_s N$ and solve for $\mu_s$:

$\mu_s = \frac{F_c}{N}$

Using $F_c = \frac{mv^2}{r}$ and $N=mg$, where g is the acceleration due to gravity, we get:

$\mu_s = \frac{v^2}{gr}$

Substituting the given values, we get:

$\mu_s = \frac{(40.0	ext{ m/s})^2}{(9.81	ext{ m/s}^2)(200	ext{ m})} \approx 0.816$

Therefore, the minimum coefficient of static friction required is 0.816, which corresponds to choice (B).

Question 18

A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution?
A) 4.8 s
B) 3.8 s
C) 4.5 s
D) 5.2 s

Accepted Answer

The answer of A 23 kg mass is connected to...

Question 19

A 600-kg car traveling at 30.0 m/s is going around a curve having a radius of 120 m that is banked at an angle of 25.0°. The coefficient of static friction between the car's tires and the road is 0.300. What is the magnitude of the force exerted by friction on the car?
A) 1590 N
B) 3430 N
C) 7240 N
D) 7820 N
E) 795 N

Accepted Answer

The answer of A 600-kg car traveling at 30.0 m/s...

Question 20

A string is attached to the rear-view mirror of a car. A ball is hanging at the other end of the string. The car is driving around in a circle, at a constant speed. Which of the following lists gives all of the forces directly acting on the ball?
A) tension and gravity
B) tension
C) tension, gravity, and the centripetal force
D) tension, gravity, the centripetal force, and friction

Accepted Answer

The only forces acting on the ball are tension (from the string) and gravity. The centripetal force is not a separate force, but rather the net force that is required to keep the ball moving in a circular path. Friction is likely present, but it is not directly acting on the ball itself.

Quiz 8: Dynamics Ii: Motion in a Plane

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station 390 m diameter rotating about its central axis. Astronauts walk on the inside surface of the space station. What rotation period will provide "normal" gravity?

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

Engineers are designing a curved section of a highway. If the radius of curvature of the curve is at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?

A car drives over a hilltop that has a radius of curvature 0.120 km at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

Suppose a highway curve is properly banked to eliminate friction for a speed of 45 mph. If your tires were bald and you wanted to avoid sliding on the road, you would have to drive

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out because an outward force balances the pull of gravity on the water.

The figure shows two wires that are tied to a 710 g mass that revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in the upper wire?

The figure shows two wires tied to a 3.3 kg sphere that revolves in a horizontal circle at constant speed. At this particular speed the tension is the SAME in both wires. What is the tension?

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m. What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?

A 600-kg car traveling at 30.0 m/s is going around a curve having a radius of 120 m that is banked at an angle of 25.0°. The coefficient of static friction between the car's tires and the road is 0.300. What is the magnitude of the force exerted by friction on the car?

A string is attached to the rear-view mirror of a car. A ball is hanging at the other end of the string. The car is driving around in a circle, at a constant speed. Which of the following lists gives all of the forces directly acting on the ball?