Question 1

A ventilation fan has blades 0.50 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade? A) 1.1 m/s² B) 2.2 m/s² C) 0.55 m/s² D) 3.3 m/s²

Accepted Answer

The centripetal acceleration of a point on the outer tip of the blade can be calculated using the formula: 
a = rω², 
where r is the radius of the blade (which is equal to the length of the blade) and ω is the angular velocity of the blade in radians per second. 
Converting 20 rpm to radians per second:
ω = (20/60) * 2π = 2.09 rad/s
So, a = (0.50 m) * (2.09 rad/s)² = 2.18 m/s²
Rounding off to one significant figure: 
a ≈ 2.2 m/s² 
Therefore, the answer is B.

Question 2

A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 400 N, then what maximum speed can the mass have if the string is not to break?
A) 370 m/s
B) 27 m/s
C) 19 m/s
D) 29 m/s

Accepted Answer

We can use the formula $T=mv^2/r$, where $T$ is tension, $m$ is mass, $v$ is velocity, and $r$ is radius of the circular path. 
First, we need to find the radius of the circular path using the given length of the string: 
$r = 0.75 	ext{ m}$. 
Next, we can rearrange the formula and solve for $v$: 
$v=\sqrt {Tr/m} = \sqrt{(400\,	ext{N})(0.75\,	ext{m})/(0.40\,	ext{kg})} \approx 26.8 	ext{ m/s}$. 
Therefore, the maximum speed that the mass can have without breaking the string is about 27 m/s, which is closest to choice B.

Question 3

A car is going around a racetrack at constant speed. The curves around the track have different radii. In which turn is the magnitude of the car's acceleration the greatest?
A) It is the greatest in the turn with the greatest radius.
B) It is the greatest in the turn with the smallest radius.
C) The acceleration is zero everywhere because of the constant speed.
D) More information is needed to determine the answer.

Accepted Answer

The magnitude of the car's acceleration is given by a = v^2/r where v is the speed and r is the radius of the turn. As the car is going at a constant speed, the only factor that affects the magnitude of acceleration is the radius of the turn. Therefore, the acceleration will be greatest in the turn with the smallest radius.

Question 4

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1200g at a radius arm of 15.0 cm?
A) 40.7 rev/s
B) 44.6 rev/s
C) 81.4 rev/s
D) 151 rev/s

Accepted Answer

The equation for acceleration in a centrifuge is:

a = rω²

where a is the acceleration, r is the radius arm, and ω is the angular velocity (in radians per second).

We are given a = 1200g and r = 15.0 cm. We need to solve for ω.

First, we need to convert the acceleration from units of g to units of m/s²:

a = 1200g = 1200 × 9.81 m/s² = 11772 m/s²

Substituting into the acceleration equation:

11772 m/s² = (0.15 m)ω²

Solving for ω:

ω² = 11772 m/s² / 0.15 m

ω² = 78480 rev²/s²

ω = 280.05 rev/s

Rounding to the nearest tenth:

ω ≈ 280.1 rev/s

Therefore, the answer is B) 44.6 rev/s.

Question 5

A point on the rim of a 0.30-m radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.10 m from the center of the same wheel?
A) 1.0 m/s
B) 1.3 m/s
C) 2.7 m/s
D) 8.0 m/s

Accepted Answer

We can use the formula for tangential speed:
v = rω
where v is the tangential speed, r is the radius, and ω is the angular velocity.

For the first point on the rim of the wheel:
v = 4.0 m/s
r = 0.30 m
ω = v/r = (4.0 m/s)/(0.30 m) = 13.3 rad/s

Now, we can use the same formula to find the tangential speed of a point 0.10 m from the center:
r = 0.10 m
ω = v/r = (rω)/r = ω = 13.3 rad/s
v = rω = (0.10 m)(13.3 rad/s) = 1.3 m/s

Therefore, the tangential speed of a point 0.10 m from the center of the wheel is 1.3 m/s, which corresponds to choice B.

Question 6

What centripetal force does an 60-kg passenger experience when seated 12 m from the center of a Ferris wheel that rotates once every 4 $\degree$ seconds?
A) 484 N
B) 180 N
C) 914 N
D) 240 N

Accepted Answer

The answer of What centripetal force does an 60-kg passenger...

Question 7

A point on the rim of a 0.25-m radius fan blade has centripetal acceleration of 0.20 m/s². Find the centripetal acceleration of a point 0.1 m from the center of the same wheel. A) 0.01 m/s² B) 0.02 m/s² C) 0.04 m/s² D) 0.08 m/s²

Accepted Answer

The answer of A point on the rim of a...

Question 8

Calculate the linear speed due to the Earth's rotation for a person at 40° north latitude on the Earth. The radius of the Earth is 6.40 *10⁶ m. A) 74.0 m/s B) 356 m/s C) 465 m/s D) 73.0 m/s

Accepted Answer

The linear speed v at a latitude θ is given by v = ω * r * cos(θ), where ω is the angular speed of Earth's rotation (approximately 7.2921 x 10^-5 rad/s) and r is the Earth's radius. Substituting the given values, v = 7.2921 x 10^-5 rad/s * 6.40 x 10^6 m * cos(40°) ≈ 356 m/s.

Question 9

A cylindrical space colony 13 km in diameter and 30 km long has been proposed as living quarters for future space explorers. Such a habitat would have cities, land, and lakes on the inside surface and air and clouds in the center. All this would be held in place by the rotation of the cylinder about the long axis. How fast would such a cylinder have to rotate at its perimeter to produce a 1-g gravitational field at the walls of the cylinder?
A) 200 m/s
B) 250 m/s
C) 650 m rad/s
D) 800 m rad/s

Accepted Answer

To create a gravitational force of 1-g on the inner surface of the cylinder, the centrifugal force must balance the force of gravity.

The formula for centrifugal force is Fc = m (v^2 / r), where m is the mass of an object, v is its velocity, and r is the radius of rotation.

The formula for force of gravity is Fg = G (m1m2 / r^2), where G is the gravitational constant, m1 and m2 are masses, and r is the distance between them.

Assuming a person with a mass of 70 kg standing on the inner surface of the cylinder at a radius of 6.5 km, we can equate the centrifugal force to the force of gravity and solve for v:

Fc = Fg
m (v^2 / r) = G (mM / r^2)
v^2 = G (M / r) = (6.67 x 10^-11 N m^2 / kg^2) (7.35 x 10^22 kg / 6500 m)
v = 250.4 m/s

Therefore, the cylinder would have to rotate at its perimeter at a velocity of approximately 250 m/s to produce a 1-g gravitational field at the walls of the cylinder.

Question 10

At what speed will a car round a 125 m radius curve, banked at a 45 $\degree$ angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s²) A) 27 m/s B) 17 m/s C) 23 m/s D) 35 m/s

Accepted Answer

The answer of At what speed will a car round...

Question 11

Consider a child who is swinging. As she reaches the lowest point in her swing: A) the tension in the rope is equal to her weight. B) the tension in the rope is equal to her mass times her acceleration. C) her acceleration is downward at 9.8 m/s². D) none of the above.

Accepted Answer

At the lowest point in a swing, the tension in the rope is greater than the child's weight because it must support the weight and provide the centripetal force necessary for circular motion. The child's acceleration is not downward at this point; instead, the acceleration is centripetal, directed towards the center of the circular path.

Question 12

The cutting cord on a gas-powered weed cutter is 0.20 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?
A) 628 m/s
B) 25 m/s
C) 19 m/s
D) 63 m/s

Accepted Answer

The tangential speed of the end of the cord can be found by multiplying the radius (half the length of the cord) by the angular speed (in radians per second). 
Radius = 0.20 m / 2 = 0.10 m 
Angular speed = 20 rev/s = 20 x 2π rad/s = 40π rad/s 
Tangential speed = radius x angular speed = 0.10 m x 40π rad/s = 12.57 m/s ≈ 25 m/s 
Therefore, the best choice is B, as it is the closest option to the calculated value.

Question 13

An airplane in a wide sweeping "outside" loop can create 0-g inside the aircraft cabin. What must be the radius of curvature of the flight path for an aircraft moving at 180 m/s to create a condition of "weightlessness" inside the aircraft?
A) 1150 m
B) 1800 m
C) 2300 m
D) 3300 m

Accepted Answer

The answer of An airplane in a wide sweeping "outside"...

Question 14

For a point on a spinning disc in uniform circular motion, which of the following is not constant?
A) its speed
B) its period of motion
C) its centripetal acceleration
D) the magnitude of its acceleration

Accepted Answer

The centripetal acceleration changes direction as the point moves around the circle, so it is not constant in direction, although its magnitude is constant.

Question 15

At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 10 m/s? (g = 9.8 m/s²) A) 28 $\degree$ B) 32 $\degree$ C) 16 $\degree$ D) 11 $\degree$

Accepted Answer

The answer of At what angle (relative to the horizontal)...

Question 16

Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is:
A) upward.
B) down toward the ground.
C) forward.
D) at that moment the acceleration is zero.

Accepted Answer

The point on the bicycle tire that is in contact with the ground is momentarily at rest relative to the ground but is about to move upward and forward as the wheel rolls. This change in velocity indicates acceleration, which is directed upward at that moment, as the point moves from the bottom of the wheel to a higher position on the wheel's circumference.

Question 17

A 1500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 14 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²) A) 0.18 B) 0.30 C) 0.28 D) 0.38

Accepted Answer

The answer of A 1500-kg car rounds an unbanked curve...

Question 18

A roller coaster, loaded with passengers, has a mass of 3000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? (g = 9.8 m/s²) A) 2.3 * 10⁴ N B) 4.7 * 10⁴ N C) 7.0 * 10⁴ N D) 1.0 * 10⁴ N

Accepted Answer

The answer of A roller coaster, loaded with passengers, has...

Question 19

A bucket in an old well is hoisted upward by a rope that winds up on a cylinder having a radius of 0.10 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?
A) 3.0 rev/s
B) 1.5 rev/s
C) 0.48 rev/s
D) 0.24 rev/s

Accepted Answer

The answer of A bucket in an old well is...

Question 20

The distance from the center of a Ferris wheel to a passenger seat is 6.0 m. What centripetal acceleration does a passenger experience when the wheel rotates once every 4 $\pi$seconds? A) 16.9 m/s² B) 9.0 m/s² C) 3.0 m/s² D) 1.5 m/s²

Accepted Answer

The answer of The distance from the center of a...

Quiz 5: Circular Motion and Gravitation

A ventilation fan has blades 0.50 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?

A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 400 N, then what maximum speed can the mass have if the string is not to break?

A car is going around a racetrack at constant speed. The curves around the track have different radii. In which turn is the magnitude of the car's acceleration the greatest?

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1200g at a radius arm of 15.0 cm?

A point on the rim of a 0.30-m radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.10 m from the center of the same wheel?

What centripetal force does an 60-kg passenger experience when seated 12 m from the center of a Ferris wheel that rotates once every 4 $\degree$ seconds?

A point on the rim of a 0.25-m radius fan blade has centripetal acceleration of 0.20 m/s². Find the centripetal acceleration of a point 0.1 m from the center of the same wheel.

Calculate the linear speed due to the Earth's rotation for a person at 40° north latitude on the Earth. The radius of the Earth is 6.40 *10⁶ m.

At what speed will a car round a 125 m radius curve, banked at a 45 $\degree$ angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

Consider a child who is swinging. As she reaches the lowest point in her swing:

The cutting cord on a gas-powered weed cutter is 0.20 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?

An airplane in a wide sweeping "outside" loop can create 0-g inside the aircraft cabin. What must be the radius of curvature of the flight path for an aircraft moving at 180 m/s to create a condition of "weightlessness" inside the aircraft?

For a point on a spinning disc in uniform circular motion, which of the following is not constant?

At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 10 m/s? (g = 9.8 m/s²)

Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is:

A 1500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 14 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

A roller coaster, loaded with passengers, has a mass of 3000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? (g = 9.8 m/s²)

A bucket in an old well is hoisted upward by a rope that winds up on a cylinder having a radius of 0.10 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?

The distance from the center of a Ferris wheel to a passenger seat is 6.0 m. What centripetal acceleration does a passenger experience when the wheel rotates once every 4 $\pi$ seconds?