Question 1

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

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Question 2

An 80.0-kg object is falling and experiences a drag force due to air resistance.The magnitude of this drag force depends on its speed,v,and obeys the equation  What is the terminal speed of this object?

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Question 3

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  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.

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Question 4

A roadway for stunt drivers is designed for racecars moving at a speed of  .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?

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Question 5

A 1.20-kg ball is hanging from the end of a rope.The rope hangs at an angle 25.0° from the vertical when a 15.0 m/s horizontal wind is blowing.If the wind's force on the rope is negligible,what drag force does the wind exert on the ball?

Accepted Answer

The drag force exerted by the wind on the ball can be found by analyzing the forces acting on the ball. The tension in the rope has a vertical component that balances the weight of the ball and a horizontal component that equals the drag force of the wind. The weight of the ball is $mg = 1.20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 11.76 \, \text{N}$. Since the rope makes an angle of 25.0° with the vertical, the horizontal component (drag force) can be found using trigonometry: $\tan(25.0°) = \frac{\text{Drag Force}}{11.76 \, \text{N}}$. Solving for the drag force gives approximately 5.48 N.

Question 6

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?

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 7

A 30.0-kg object experiences a drag force due to air resistance with a magnitude proportional to the square of its speed.The object falls with an acceleration of  downward when it is falling downward at  .What is its terminal speed?

Accepted Answer

We can use the equation for the net force on the object:

F_net = m*a = m*g - kv^2

where m is the mass of the object, g is the acceleration due to gravity (9.81 m/s^2), k is the constant of proportionality for the drag force, and v is the speed of the object.

At terminal speed, the acceleration is zero, so we have:

0 = m*g - kv_terminal^2

Solving for v_terminal, we get:

v_terminal = sqrt(m*g/k)

Substituting in the given values, we get:

v_terminal = sqrt((30.0 kg)*(9.81 m/s^2)/((30.0 kg/s^2)*(11.0 m/s)))

v_terminal = 91.0 m/s

Therefore, the answer is (C) 91.0 m/s.

Question 8

A ship is being pulled through a harbor at constant velocity by two tugboats as shown in the figure.The lines attached to the two tugboats have the same tension of 200,000 N.Each line makes an angle of 28.0° with the direction the ship is being towed.What is the magnitude of the drag force due to the water on the ship?

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Question 9

The figure shows two forces acting on an object,with magnitudes  and  What third force will cause the object to be in equilibrium (acceleration equals zero)?

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Question 10

An object weighing 4.00 N falls from rest subject to a frictional drag force given by  ,where v is the speed of the object and  What terminal speed will this object approach?

Accepted Answer

The drag force is given by F_d = bv^2 where b = 11ea83ea_698b_8ac1_aeff_a1a4c9aaa927_TB6394_11. The net force acting on the object is F_net = ma = mg - bv^2, where m is the mass of the object and g is the acceleration due to gravity. When the object reaches terminal velocity, its speed is constant, so the net force acting on it is zero. Therefore, we have:

mg - bv_t^2 = 0

Solving for v_t, we get:

v_t = sqrt(g/b) = sqrt(4.00 N / (11ea83ea_698b_8ac1_aeff_a1a4c9aaa927_TB6394_11)) = 1.15 m/s

Therefore, the answer is choice C.

Question 11

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?

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Question 12

A person on a sled coasts down a hill and then goes over a slight rise with speed  .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?

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Question 13

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?

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Question 14

The magnitude of the drag force of air resistance on a certain 20.0-kg object is proportional to its speed.If the object has a terminal speed of  ,what is the magnitude of the drag force on the object when it is falling with a speed of  ?

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Question 15

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

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Quiz 5: Applying Newtons Laws

An 80.0-kg object is falling and experiences a drag force due to air resistance.The magnitude of this drag force depends on its speed,v,and obeys the equation What is the terminal speed of this object?

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 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 roadway for stunt drivers is designed for racecars moving at a speed of .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 1.20-kg ball is hanging from the end of a rope.The rope hangs at an angle 25.0° from the vertical when a 15.0 m/s horizontal wind is blowing.If the wind's force on the rope is negligible,what drag force does the wind exert on the ball?

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 30.0-kg object experiences a drag force due to air resistance with a magnitude proportional to the square of its speed.The object falls with an acceleration of downward when it is falling downward at .What is its terminal speed?

The figure shows two forces acting on an object,with magnitudes and What third force will cause the object to be in equilibrium (acceleration equals zero) ?

An object weighing 4.00 N falls from rest subject to a frictional drag force given by ,where v is the speed of the object and What terminal speed will this object approach?

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?

The magnitude of the drag force of air resistance on a certain 20.0-kg object is proportional to its speed.If the object has a terminal speed of ,what is the magnitude of the drag force on the object when it is falling with a speed of ?

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