Question 1

The moon Demos takes 30 hours 26 minutes to complete one orbit around Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,what is the radius of Demos' orbit around Mars? A)4.08 * 10⁶ m B)2.56 * 10⁵ m C)8.69 * 10⁶ m D)1.47 * 10⁸ m E)2.35 * 10⁷ m

Accepted Answer

The answer of The moon Demos takes 30 hours 26...

Question 2

A flatbed truck goes around a curve of radius R with speed V.There is a box on the truck of M kg mass.Which statement is correct concerning the net horizontal force on the box,if the box does not slide? A)It is MV²/R outward from the center of the curve. B)It is zero. C)It is MV²/R inward towards the center of the curve. D)It is MgR outward from the center of the curve. E)It is MgR inward towards the center of the curve.

Accepted Answer

The net horizontal force on the box is in the direction of the centripetal force required to keep it moving in a circular path. This force is given by F = Mv^2/R, where M is the mass of the box, v is the speed of the truck, and R is the radius of the curve. Since the box is not sliding, the force of friction between the box and the truck is also in this direction. Therefore, the net horizontal force on the box is inward towards the center of the curve. Choice C is the only option that reflects this.

Question 3

A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L.The mass is pulled back,raised and released.If the tension in the string at the bottom of the swing is 2mg,how high was the the mass raised above the bottom of the swing?
A)0.33 L
B)0.25 L
C)0.10 L
D)0.50 L
E)0.67 L

Accepted Answer

At the bottom of the swing, the tension in the string is the sum of the centripetal force needed to keep the mass moving in a circular path and the gravitational force acting on the mass. The tension is given as $2mg$, which means the centripetal force component is $mg$, since the gravitational force $mg$ is also acting on the mass. The centripetal force can be equated to the change in potential energy, which is $mgh$, where $h$ is the height raised. Since the centripetal force is $mg$, and it equals $mgh$, we have $mg = mgh$, which simplifies to $h = \frac{1}{2}L$, indicating the mass was raised to a height of $0.5L$ above the bottom of the swing.

Question 4

Two masses are attached to a 1-meter rope as shown such that half of the rope hangs vertically below the frictionless table.m₁ (= 2 kg)is set into circular motion with speed 3.0 m/s.What is the value of m₂ if m₂ is to remain stationary? A)5.2 kg B)4.6 kg C)3.7 kg D)2.5 kg E)2.0 kg

Accepted Answer

The answer of Two masses are attached to a 1-meter...

Question 5

Somewhere on the surface of the Earth a yo-yo with m = 0.050 kg is swung in a vertical circle with radius r = 0.40 m.Find the tension on the string at the top if the speed at that point is v = 2.0 m/s.
A)3.0 N
B)27.0 N
C)81.0 N
D)0.333 N
E)0.0095 N

Accepted Answer

The answer of Somewhere on the surface of the Earth...

Question 6

A toy train moves with uniform speed on a circular track.Which of the following statements is true?
A)The angular acceleration is always positive.
B)The angular acceleration is always negative.
C)The angular acceleration can either be positive or negative,depending if the train runs clockwise or counter-clockwise.
D)The centripetal acceleration is 0.
E)The centripetal acceleration does not change in magnitude.

Accepted Answer

Since the train moves with uniform speed, its velocity is constant in magnitude and direction. Therefore, the acceleration is entirely due to the centripetal acceleration, which points towards the center of the circular track. The magnitude of the centripetal acceleration is given by a = v^2/r, where v is the speed of the train and r is the radius of the track. Since both v and r are constant, the magnitude of the centripetal acceleration is also constant, and therefore, the best choice is E, which states that the centripetal acceleration does not change in magnitude. The other choices are incorrect because the angular acceleration is not necessarily constant or in a particular direction, and the centripetal acceleration is non-zero and constant.

Question 7

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height),and its speed is v = 5.54 m/s,calculate the magnitude of the total force acting on the mass.(in N) A)4.91 * 10¹ B)5.82 * 10¹ C)9.81 D)2.22 * 10¹ E)2.45 * 10¹

Accepted Answer

The answer of A small object with a mass of...

Question 8

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's centripetal acceleration,if it makes one revolution every 90 min? (The radius of Earth is approximately 6400 km.) A)1.12 m/s² B)2.69 m/s² C)5.20 m/s² D)9.34 m/s² E)9.81 m/s²

Accepted Answer

The answer of A spy satellite is in circular orbit...

Question 9

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's orbital speed,if it makes one revolution every 90 min? (You might want to know that the radius of the Earth is approximately 6400 km).
A)1 km/s
B)2 km/s
C)4 km/s
D)8 km/s
E)16 km/s

Accepted Answer

The orbital speed $v$ of a satellite is given by the formula $v = \frac{2\pi r}{T}$, where $r$ is the radius of the orbit, and $T$ is the orbital period. The radius of the orbit is the sum of the Earth's radius and the altitude of the satellite, which is $6400 \, \text{km} + 500 \, \text{km} = 6900 \, \text{km}$. The orbital period $T$ is 90 minutes, which is $1.5$ hours or $5400$ seconds. Plugging these values into the formula gives $v = \frac{2\pi \times 6900}{5400} \approx 8 \, \text{km/s}$.

Question 10

A wheel of radius 4 m is spinning with a constant angular velocity of 2 rad/s.What is the centripetal acceleration of a point on the wheel's rim? A)2 m/s² B)4 m/s² C)8 m/s² D)16 m/s² E)32 m/s²

Accepted Answer

Centripetal acceleration is given by the formula $ a_c = \omega^2 \times r $. Here, $ \omega = 2 \, \text{rad/s} $ and $ r = 4 \, \text{m} $. So, $ a_c = (2)^2 \times 4 = 16 \, \text{m/s}^2 $.

Question 11

The moon Demos is 23,500 km from Mars and orbits once every 30 hours 26 minutes.Assuming that it orbits in a circular path,what is its average speed?
A)0 m/s
B)215 m/s
C)732 m/s
D)1348 m/s
E)53,210 m/s

Accepted Answer

The answer of The moon Demos is 23,500 km from...

Question 12

Two masses are attached to a 1-meter rope as shown such that part of the rope hangs vertically below the frictionless table.m₁ (= 2 kg)is set into circular motion with speed 3.0 m/s.What is the length of rope hanging vertically below the table if tension in the rope if m₂ (= 5 kg)is to remain stationary? A)0.18 m B)0.60 m C)0.82 m D)0.71 m E)0.29 m

Accepted Answer

The answer of Two masses are attached to a 1-meter...

Question 13

A runner is running on a circular track,which is 200 m in circumference.Find the magnitude of his acceleration when he is running at a constant speed of 10.8 m/s. A)108 m/s² B)10.8 m/s² C)18.5 m/s² D)3.66 m/s² E)200 m/s²

Accepted Answer

We know that acceleration is the rate of change of velocity. In this problem, the runner is running at a constant speed of 10.8 m/s, which means the velocity is not changing, and hence the acceleration is zero.

Therefore, none of the answer choices are correct.

Question 14

Two masses are attached to a 1-meter rope as shown such that one quarter of the rope hangs vertically below the frictionless table.m₁ (= 2 kg)is set into circular motion with speed 3.0 m/s.What is the tension in the rope if m₂ is to remain stationary? A)36 N B)18 N C)28 N D)14 N E)24 N

Accepted Answer

The answer of Two masses are attached to a 1-meter...

Question 15

The moon Demos is 23,500 km from Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,how much time does it take Demos to complete one orbit? A)1.10 * 10⁵ s B)4.89 * 10³ s C)7.11 * 10⁵ s D)9.54 * 10⁵ s E)1.74 * 10⁴ s

Accepted Answer

The correct answer is A.The time period of an orbit is given by:T = 2πr / vwhere r is the radius of the orbit and v is the speed of the object.In this case, r = 23,500 km = 23,500,000 m and v = 1348 m/s.Therefore, T = 2π(23,500,000 m) / 1348 m/s = 1.10 * 10^5 s.

Question 16

On a curved roadway of radius 100 m,the suggested speed limit is 35 mph (approximately 16 m/s).What must the coefficient of friction be between a car's tires and the road for the car to safely negotiate the curve at the posted speed?
A)0.72
B)0.51
C)0.26
D)0.40
E)0.13

Accepted Answer

The centripetal force required to keep the car on the curve is given by F=mv²/r, where m is the mass of the car, v is its speed, and r is the radius of the curve. The force of friction between the tires and the road provides this centripetal force. The maximum friction force that can be exerted is given by the coefficient of friction μ times the normal force (the weight of the car in this case). Therefore, we have μmg=mv²/r, where g is the acceleration due to gravity. Solving for μ, we get μ=v²/(rg)=(16 m/s)²/[(100 m)(9.81 m/s²)]=0.26. Therefore, the coefficient of friction must be at least 0.26 for the car to safely negotiate the curve at the posted speed of 35 mph.

The best choice is C.

Question 17

An amusement park ride has a diameter of 16 meters and revolves at 15 rpm (revolutions per minute).How fast is a rider moving if she sits at the outermost part of the ride?
A)29.4 m/s
B)1.07 m/s
C)225 m/s
D)9.81 m/s
E)12.6 m/s

Accepted Answer

The circumference of the ride is π times the diameter, which is 16π meters. At 15 revolutions per minute, the speed is 15 * 16π meters per minute. Converting to meters per second, the speed is (15 * 16π) / 60 = 12.6 m/s.

Question 18

It takes a runner 10 seconds to run the curve (100 meter arc length,semicircle)in a race.The centripetal acceleration acting on her is A)1.00 m/s². B)1.57 m/s². C)1.92 m/s². D)3.14 m/s². E)3.59 m/s².

Accepted Answer

The answer of It takes a runner 10 seconds to...

Quiz 9: Circular Motion

The moon Demos takes 30 hours 26 minutes to complete one orbit around Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,what is the radius of Demos' orbit around Mars?

A flatbed truck goes around a curve of radius R with speed V.There is a box on the truck of M kg mass.Which statement is correct concerning the net horizontal force on the box,if the box does not slide?

A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L.The mass is pulled back,raised and released.If the tension in the string at the bottom of the swing is 2mg,how high was the the mass raised above the bottom of the swing?

Two masses are attached to a 1-meter rope as shown such that half of the rope hangs vertically below the frictionless table.m₁ (= 2 kg) is set into circular motion with speed 3.0 m/s.What is the value of m₂ if m₂ is to remain stationary?

Somewhere on the surface of the Earth a yo-yo with m = 0.050 kg is swung in a vertical circle with radius r = 0.40 m.Find the tension on the string at the top if the speed at that point is v = 2.0 m/s.

A toy train moves with uniform speed on a circular track.Which of the following statements is true?

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height) ,and its speed is v = 5.54 m/s,calculate the magnitude of the total force acting on the mass.(in N)

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's centripetal acceleration,if it makes one revolution every 90 min? (The radius of Earth is approximately 6400 km.)

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's orbital speed,if it makes one revolution every 90 min? (You might want to know that the radius of the Earth is approximately 6400 km) .

A wheel of radius 4 m is spinning with a constant angular velocity of 2 rad/s.What is the centripetal acceleration of a point on the wheel's rim?

The moon Demos is 23,500 km from Mars and orbits once every 30 hours 26 minutes.Assuming that it orbits in a circular path,what is its average speed?

A runner is running on a circular track,which is 200 m in circumference.Find the magnitude of his acceleration when he is running at a constant speed of 10.8 m/s.

Two masses are attached to a 1-meter rope as shown such that one quarter of the rope hangs vertically below the frictionless table.m₁ (= 2 kg) is set into circular motion with speed 3.0 m/s.What is the tension in the rope if m₂ is to remain stationary?

The moon Demos is 23,500 km from Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,how much time does it take Demos to complete one orbit?

On a curved roadway of radius 100 m,the suggested speed limit is 35 mph (approximately 16 m/s) .What must the coefficient of friction be between a car's tires and the road for the car to safely negotiate the curve at the posted speed?

An amusement park ride has a diameter of 16 meters and revolves at 15 rpm (revolutions per minute) .How fast is a rider moving if she sits at the outermost part of the ride?

It takes a runner 10 seconds to run the curve (100 meter arc length,semicircle) in a race.The centripetal acceleration acting on her is

Quiz 9: Circular Motion

The moon Demos takes 30 hours 26 minutes to complete one orbit around Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,what is the radius of Demos' orbit around Mars?

A flatbed truck goes around a curve of radius R with speed V.There is a box on the truck of M kg mass.Which statement is correct concerning the net horizontal force on the box,if the box does not slide?

A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L.The mass is pulled back,raised and released.If the tension in the string at the bottom of the swing is 2mg,how high was the the mass raised above the bottom of the swing?

Two masses are attached to a 1-meter rope as shown such that half of the rope hangs vertically below the frictionless table.m1 (= 2 kg) is set into circular motion with speed 3.0 m/s.What is the value of m2 if m2 is to remain stationary?

Somewhere on the surface of the Earth a yo-yo with m = 0.050 kg is swung in a vertical circle with radius r = 0.40 m.Find the tension on the string at the top if the speed at that point is v = 2.0 m/s.

A toy train moves with uniform speed on a circular track.Which of the following statements is true?

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height) ,and its speed is v = 5.54 m/s,calculate the magnitude of the total force acting on the mass.(in N)

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's centripetal acceleration,if it makes one revolution every 90 min? (The radius of Earth is approximately 6400 km.)

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's orbital speed,if it makes one revolution every 90 min? (You might want to know that the radius of the Earth is approximately 6400 km) .

A wheel of radius 4 m is spinning with a constant angular velocity of 2 rad/s.What is the centripetal acceleration of a point on the wheel's rim?

The moon Demos is 23,500 km from Mars and orbits once every 30 hours 26 minutes.Assuming that it orbits in a circular path,what is its average speed?

A runner is running on a circular track,which is 200 m in circumference.Find the magnitude of his acceleration when he is running at a constant speed of 10.8 m/s.

Two masses are attached to a 1-meter rope as shown such that one quarter of the rope hangs vertically below the frictionless table.m1 (= 2 kg) is set into circular motion with speed 3.0 m/s.What is the tension in the rope if m2 is to remain stationary?

The moon Demos is 23,500 km from Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,how much time does it take Demos to complete one orbit?

On a curved roadway of radius 100 m,the suggested speed limit is 35 mph (approximately 16 m/s) .What must the coefficient of friction be between a car's tires and the road for the car to safely negotiate the curve at the posted speed?

An amusement park ride has a diameter of 16 meters and revolves at 15 rpm (revolutions per minute) .How fast is a rider moving if she sits at the outermost part of the ride?

It takes a runner 10 seconds to run the curve (100 meter arc length,semicircle) in a race.The centripetal acceleration acting on her is

Two masses are attached to a 1-meter rope as shown such that half of the rope hangs vertically below the frictionless table.m₁ (= 2 kg) is set into circular motion with speed 3.0 m/s.What is the value of m₂ if m₂ is to remain stationary?

Two masses are attached to a 1-meter rope as shown such that one quarter of the rope hangs vertically below the frictionless table.m₁ (= 2 kg) is set into circular motion with speed 3.0 m/s.What is the tension in the rope if m₂ is to remain stationary?