Question 1

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

D

Question 2

If a planet has 9 times the radius of the Earth,but has the same density as the Earth,what is the gravitational acceleration at the surface of the planet? (g = 9.8 m/s²) A) 29.4 m/s² B) 88.2 m/s² C) 265 m/s² D) 39.2 m/s²

Accepted Answer

The gravitational acceleration is proportional to the radius of the planet if the density is constant. Since the radius is 9 times that of Earth, the gravitational acceleration is 9 times Earth's gravity: 9 * 9.8 m/s² = 88.2 m/s².

Question 3

An Earth satellite is orbiting at a distance from the Earth's surface equal to two Earth radii.At this location,the acceleration due to gravity is what factor times the value of g at the Earth's surface?
A) There is no acceleration since the satellite is in orbit.
B) 1/9
C) 1/4
D) The answer is not given.

Accepted Answer

B

Question 4

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

Tangential speed is directly proportional to radial distance from the center of rotation. Using the equation v = rω, where v is tangential speed, r is radial distance, and ω is angular velocity, we can solve for the tangential speed of the point 0.10 m from the center:

v = rω
v = (0.10 m)(4.0 m/s)/(0.30 m)
v = 1.3 m/s

Therefore, the correct answer is choice B.

Question 5

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 4π seconds? A) 16.9 m/s² B) 9.0 m/s² C) 3.0 m/s² D) 1.5 m/s²

Accepted Answer

The centripetal acceleration $ a_c $ is given by $ a_c = \frac{v^2}{r} $. The velocity $ v $ can be found using $ v = \frac{2\pi r}{T} $, where $ T = 4\pi $ seconds and $ r = 6.0 $ m. Substituting these values, $ v = \frac{2\pi \times 6}{4\pi} = 3 $ m/s. Thus, $ a_c = \frac{3^2}{6} = 1.5 $ m/s².

Question 6

In order to train for a high-g environment,an astronaut is placed in a centrifuge of radius several meters and rotated in a horizontal circle at constant speed.In this situation,in which direction is the net force on the astronaut?
A) The net force is down since gravity cannot be turned off.
B) The net force is horizontal toward the center of the circle.
C) The net force is between horizontal toward the center of the circle and straight up,the angle depending on the speed and the radius involved.
D) The net force is zero since the astronaut is moving at constant speed and thus the force has no direction.

Accepted Answer

The net force on the astronaut is horizontal toward the center of the circle because the astronaut is experiencing centripetal force, which always points toward the center of the circular motion. This force is not due to gravity, but rather due to the tension in the astronaut's body and the seat in the centrifuge pulling them inward. Gravity is still present, but it is not the source of the net force in this scenario.

Question 7

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1 200g 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 answer of How many revolutions per second are needed...

Question 8

What centripetal force does an 60-kg passenger experience when seated 12 m from the center of a Ferris wheel that rotates once every 4π 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 9

At what speed will a car round a 125 m radius curve,banked at a 45° 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 10

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 force exerted by the track is the sum of the gravitational force and the centripetal force. The gravitational force is mg = 3000 kg * 9.8 m/s² = 29400 N. The centripetal force is mv²/r = 3000 kg * (18 m/s)² / 24 m = 40500 N. The total force is 29400 N + 40500 N = 69900 N, which is approximately 7.0 × 10⁴ N.

Question 11

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

The answer of A 0.40-kg mass,attached to the end of...

Question 12

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N.The radius of the planet is 4.0 × 10⁶ m.What is the mass of Planet X? (G = 6.67 × 10−¹¹ N × m²/kg²) A) 13 × 10¹⁹ kg B) 17 × 10²² kg C) 9.6 × 10²⁴ kg D) 4.8 × 10²⁴ kg

Accepted Answer

The answer of An object of mass 0.50 kg is...

Question 13

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N.The radius of the planet is 4.0 × 10⁶ m.What free fall acceleration will the 0.50 kg object experience when at the surface of Planet X? A) 48 m/s² B) 20 m/s² C) 16 m/s² D) 40 m/s²

Accepted Answer

The weight of the object is given by W = mg, where m is the mass and g is the acceleration due to gravity. Given W = 10 N and m = 0.50 kg, we can solve for g: g = W/m = 10 N / 0.50 kg = 20 m/s².

Question 14

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

The answer of A cylindrical space colony 13 km in...

Question 15

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 16

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N.The radius of the planet is 4.0 × 10⁶ m.What free fall acceleration will the 0.50 kg object experience when transported to a distance of 2.0 × 10⁶ m from the surface of this planet? A) 90 m/s² B) 8.9 m/s² C) 13 m/s² D) 18 m/s²

Accepted Answer

The answer of An object of mass 0.50 kg is...

Question 17

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

Centripetal acceleration is inversely proportional to the square of the radius. So, if the radius is halved, the centripetal acceleration will be multiplied by 4.

Question 18

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 minimum coefficient of friction (μ) can be calculated using the formula for centripetal force: μ = v²/(rg). Substituting the given values: μ = (14 m/s)² / (52 m * 9.8 m/s²) = 0.38.

Question 19

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 can be calculated using the formula V = rω, where V is the tangential speed, r is the radius of the circular motion (which is the length of the cutting cord), and ω is the angular velocity (which can be calculated by multiplying the rotational speed by 2π). Plugging in the given values, we get V = 0.20 m × 20 rev/s × 2π = 25.12 m/s, which can be rounded to 25 m/s. Therefore, the correct answer is B.

Question 20

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° B) 32° C) 16° D) 11°

Accepted Answer

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

Quiz 5: Energy: Part A

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?

If a planet has 9 times the radius of the Earth,but has the same density as the Earth,what is the gravitational acceleration at the surface of the planet? (g = 9.8 m/s²)

An Earth satellite is orbiting at a distance from the Earth's surface equal to two Earth radii.At this location,the acceleration due to gravity is what factor times the value of g at the Earth's surface?

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?

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 4π seconds?

In order to train for a high-g environment,an astronaut is placed in a centrifuge of radius several meters and rotated in a horizontal circle at constant speed.In this situation,in which direction is the net force on the astronaut?

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1 200g at a radius arm of 15.0 cm?

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

At what speed will a car round a 125 m radius curve,banked at a 45° angle,if no friction is required 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 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?

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N.The radius of the planet is 4.0 × 10⁶ m.What is the mass of Planet X? (G = 6.67 × 10−¹¹ N × m²/kg²)

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N.The radius of the planet is 4.0 × 10⁶ m.What free fall acceleration will the 0.50 kg object experience when at the surface of Planet X?

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 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 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)

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?

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)