Deck 5: Further Applications of Newtons Laws

Question 1

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 500 m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?

A)0.25
B)0.50
C)1.00
D)2.00
E)4.00

Answer 1

4.00

Question 2

When a car goes around a circular curve on a level road without slipping:

A)no frictional force is needed because the car simply follows the road.
B)the frictional force of the road on the car increases when the car's speed decreases.
C)the frictional force of the road on the car increases when the car's speed increases.
D)the frictional force of the road on the car increases when the car moves to the outside of the curve.
E)there is no net frictional force because the road and the car exert equal and opposite forces on each other.

Answer 2

the frictional force of the road on the car increases when the car's speed increases.

Question 3

Frank says that if you release the string when swinging a ball in a horizontal circle, the ball flies out in the radial direction defined by the string at the instant you release the ball. John says that it flies out along a tangent line perpendicular to the string, and that it then drops straight down to the ground. Which one, if either, is correct?

A)Frank, because the centrifugal force is no longer counteracted by the string.
B)Frank, because balls naturally fly straight out.
C)John, because there is no centrifugal force.
D)John, because balls fall straight down when released.
E)Neither, because although there is no centrifugal force, and the ball's velocity is tangent to the circle at the instant of release, the ball then follows a parabolic trajectory.

Answer 3

Neither, because although there is no centrifugal force, and the ball's velocity is tangent to the circle at the instant of release, the ball then follows a parabolic trajectory.

Question 4

The coefficient of static friction for the tyres of a race car is 0.950 and the coefficient of kinetic friction is 0.800. The car is on a level circular track of 50.0 m radius on a planet where $g=2.45 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ compared to Earth's $g=9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ . If the car is to be able to travel at the same speed on the planet as on Earth, the radius of the track on the planet must be ____ times as large as the radius of the track on Earth.

A)0.250
B)0.500
C)1.00
D)2.00
E)4.00

Question 5

The Hills Motorway in Sydney has a number of lanes for traffic. For traffic going in one direction, the radius for the inside of the curve is half the radius for the outside. One car, car A, travels on the inside while another car of equal mass, car B, travels at equal speed on the outside of the curve. Which statement about resultant forces on the cars is correct?

A)The force on A is half the force on B.
B)The force on B is half the force on A.
C)The force on A is four times the force on B.
D)The force on B is four times the force on A.
E)There is no net resultant force on either as long as they stay on the road while turning.

Question 6

A roller-coaster car at a Gold Coast theme park has a mass of 500 kg when fully loaded with passengers. At the bottom of a circular dip of radius 40 m (as shown in the figure) the car has a speed of 16 m/s. What is the magnitude of the force of the track on the car at the bottom of the dip?

A)3.2 kN
B)8.1 kN
C)4.9 kN
D)1.7 kN
E)5.3 kN

Question 7

For a plane to be able to fly clockwise in a horizontal circle as seen from above, in addition to exerting a force downwards on the air:

A)it must be increasing its speed.
B)it must exert a force on the air that is directed to the plane's left side.
C)it must exert a force on the air that is directed to the plane's right side.
D)it does not need to exert a force: it must only move the wing flaps out.
E)it only needs to deflect the air without exerting any additional force on the air.

Question 8

A boy on board a cruise ship drops a 30.0 gm marble into the ocean. If the resistive force proportionality constant is 0.500 kg/s, what is the terminal speed of the marble in m/s?

A)0.147
B)0.294
C)0.588
D)1.18
E)2.35

Question 9

A skydiver of 75 kg mass has a terminal velocity of 60 m/s. At what speed is the resistive force on the skydiver half that when at terminal speed?

A)15 m/s
B)49 m/s
C)30 m/s
D)42 m/s
E)36 m/s

Question 10

A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m), as shown. At an instant when $\theta$ = 50 $\degree$ , the tension in the string is 8.0 N. What is the magnitude of the resultant force on the mass at this instant?

A)5.6 N
B)6.0 N
C)6.5 N
D)5.1 N
E)2.2 N

Question 11

Two small cylindrical plastic containers with flat bottoms are placed on a turntable that has a smooth flat surface. Canister A is empty; canister B contains lead shot. Each canister is the same distance r from the centre. The coefficient of static friction between the canisters and the turntable is $\mu$ s. When the speed of the turntable is gradually increased,

A)only the lighter container slides outward off the turntable; the heavier one stays on.
B)only the heavier container slides outward off the turntable; the lighter one stays on.
C)both containers slide off the turntable at the same turntable speed.
D)the lighter container slides inward.
E)the heavier container slides inward.

Question 12

The coefficient of static friction for the tyres of a race car is 0.950 and the coefficient of kinetic friction is 0.800. The car is on a level circular track of 50.0 m radius on a planet where $g=2.45 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ compared to Earth's $g=9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ . The maximum safe speed on the track on the planet is ____ times as large as the maximum safe speed on Earth.

A)0.250
B)0.500
C)1.00
D)2.00
E)4.00

Question 13

A race car travels 40 m/s around a banked (45 $\degree$ with the horizontal) circular (radius = 0.20 km) track. What is the magnitude of the resultant force on the 80-kg driver of this car?

A)0.68 kN
B)0.64 kN
C)0.72 kN
D)0.76 kN
E)0.52 kN

Question 14

The following equation was obtained by solving a physics problem: $\frac{\left(16.0 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}}{(75.0 \mathrm{~m})\left(9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)}=\tan 19.2^{\circ}$ The best physical representation of the situation is:

A)A car travelling at 16.0 m/s is 19.2 $\degree$ into a turn of a quarter circle on a level road.
B)A mass on a string that is originally horizontal has fallen to where the angle between the string and the vertical direction is 19.2 $\degree$ .
C)A mass on a string originally horizontal has fallen 19.2 $\degree$ from the horizontal direction.
D)A car traveling at 16.0 m/s is on a circular curve banked at 19.2 $\degree$ .
E)A car traveling at 16.0 m/s and going over a semicircular mountain-top road is 19.2 $\degree$ down from the top.

Question 15

The equation below is the solution to a problem. $\frac{(2.00 \mathrm{~kg})\left(8.00 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}}{5.00 \mathrm{~m}}=6.00 \mathrm{~N}-(2.00 \mathrm{~kg})\left(9.80 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)\left(\cos 180^{\circ}\right)$ .The best physical representation of this equation is:

A)a sphere of 2.00 kg mass under a 6.00 N tension when at the bottom of a vertical circle.
B)a sphere of 2.00 kg mass under a 6.00 N tension when at the side of a vertical circle.
C)a sphere of 2.00 kg mass under a 6.00 N tension when at the top of a vertical circle.
D)a sphere of 2.00 kg mass at any point on a horizontal circle.
E)a 2.00 kg gecko running on the ceiling with a speed of 8.00 m/s.

Question 16

A curve on the Hume highway has a radius of 0.14 km and is unbanked. A car weighing 12 kN goes around the curve at a speed of 24 m/s without slipping. What is the magnitude of the horizontal force of the road on the car?

A)12 kN
B)17 kN
C)13 kN
D)5.0 kN
E)49 kN

Question 17

A rock attached to a string swings in a vertical circle. Which free body diagram could correctly describe the force(s) on the rock when it is at the highest point?

A)
B)
C)
D)
E)

Question 18

A race car travelling at 100 m/s during a race at Bathurst enters an unbanked turn of 400 m radius. The coefficient of (static) friction between the tyres and the track is 1.1. The track has both an inner and an outer wall. Which statement is correct?

A)The race car will crash into the outer wall.
B)The race car will crash into the inner wall.
C)The car will stay in the centre of the track.
D)The car will stay in the centre of the track if the driver speeds up.
E)The car would stay in the centre of the track if the radius were reduced to 200 m.

Question 19

A wasp circles around a beer can at constant speed once per second in a path with a 12-cm diameter. We can conclude that the wasp's wings must push on the air with force components that are:

A)straight down.
B)down and inwards.
C)down and outwards.
D)down and backwards.
E)down, inwards and backwards.

Question 20

An airplane moves 140 m/s as it travels around a vertical circular loop which has a 1.0-km radius. What is the magnitude of the resultant force on the 70-kg pilot of this plane at the bottom of this loop?

A)2.1 kN
B)1.4 kN
C)0.69 kN
D)1.5 kN
E)1.3 kN

Question 21

The frictional force of the floor on a large suitcase is least when the suitcase is:

A)pushed by a force parallel to the floor.
B)dragged by a force parallel to the floor.
C)pulled by a force directed at an angle $\theta$ above the floor.
D)pushed by a force directed at an angle $\theta$ into the floor.
E)turned on its side and pushed by a force parallel to the floor.

Question 22

The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction $\mu$ k is least when the force is applied at an angle $\theta$ such that:

A)sin $\theta$ = $\mu$ k.
B)cos $\theta$ = $\mu$ k.
C)tan $\theta$ = $\mu$ k.
D)cot $\theta$ = $\mu$ k.
E)sec $\theta$ = $\mu$ k.

Question 23

If a 20-kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s?

A)9.80 m/s2
B)7.35 m/s2
C)4.90 m/s2
D)2.45 m/s2
E)More information is needed to answer this question.

Question 24

A car enters a level, unbanked semicircular hairpin turn of 100 m radius at a speed of 28 m/s. The coefficient of friction between the tyres and the road is $\mu$ = 0.800. If the car maintains a constant speed of 28 m/s, it will:

A)attempt to dig into the road surface.
B)tend to veer toward the centre of the semicircle.
C)arrive safely at the end of the semicircle.
D)tend to veer toward the outside of the circle.
E)veer toward the centre for the first quarter-circle, then veer toward the outside for the second quarter-circle.

Question 25

Two blocks are accelerated across a horizontal frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. If F = 1.2 N and M = 1.0 kg, what is the horizontal component (frictional force) of the force of the large block on the small block?

A)0.40 N to the left
B)0.80 N to the right
C)0.40 N to the right
D)0.80 N to the left
E)1.20 N to the left

Question 26

The block shown is pulled across the horizontal surface at a constant speed by the force shown. If M = 5.0 kg, F = 14 N and $\theta$ = 35 $\degree$ , what is the coefficient of kinetic friction between the block and the horizontal surface?

A)0.44
B)0.33
C)0.38
D)0.28
E)0.17

Question 27

A 2.0-kg block slides on a rough horizontal surface. A force (magnitude P = 4.0 N) acting parallel to the surface is applied to the block. The magnitude of the block's acceleration is 1.2 m/s2. If P is increased to 5.0 N, determine the magnitude of the block's acceleration.

A)2.1 m/s2
B)2.3 m/s2
C)1.9 m/s2
D)1.7 m/s2
E)3.2 m/s2

Question 28

A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide?

A)14 m
B)11 m
C)19 m
D)24 m
E)29 m

Question 29

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 1000 m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?

A)0.25
B)0.50
C)1.00
D)2.00
E)4.00

Question 30

In the figure, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is 0.30. If F = 10 N and M = 1.0 kg, what is the tension in the connecting string?

A)8.0 N
B)6.0 N
C)6.7 N
D)8.7 N
E)3.0 N

Question 31

What is the net force on a 10-kg solid steel sphere falling in air at terminal speed?

A)980 N
B)200 N
C)98 N
D)49 N
E)Some value other than those given above.

Question 32

The three blocks shown are released from rest and are observed to move with accelerations that have a magnitude of 1.5 m/s2. What is the magnitude of the friction force on the block that slides horizontally? Disregard any pulley mass or friction in the pulley and let M = 2.0 kg.

A)6.0 N
B)5.1 N
C)5.5 N
D)4.6 N
E)3.7 N

Question 33

The coefficient of kinetic friction between the surface and the larger block is 0.25, and the coefficient of kinetic friction between the surface and the smaller block is 0.40. If F = 22 N and M = 1.0 kg in the figure, what is the magnitude of the acceleration of either block?

A)1.8 m/s2
B)2.6 m/s2
C)1.4 m/s2
D)2.2 m/s2
E)3.7 m/s2

Question 34

A 3.0-kg block moves up a 40 $\degree$ incline with constant speed under the action of a 26-N force acting up and parallel to the incline. What magnitude force must act up and parallel to the incline for the block to move down the incline at constant velocity?

A)14 N
B)12 N
C)16 N
D)18 N
E)25 N

Question 35

In the figure shown, the coefficient of kinetic friction between the block and the incline is 0.29. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley.

A)5.4 m/s2
B)5.2 m/s2
C)4.9 m/s2
D)5.6 m/s2
E)7.9 m/s2

Question 36

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the speed remained the same, by what factor would its centripetal acceleration change?

A)0.25
B)0.50
C)1.00
D)2.00
E)4.00

Question 37

Two blocks are accelerated across a horizontal frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. If F = 1.2 N and M = 1.0 kg, what is the horizontal component (frictional force) of the force of the small block on the large block?

A)0.48 N to the right
B)0.72 N to the right
C)0.72 N to the left
D)0.48 N to the left
E)0.65 N to the left

Question 38

A block is pushed across a horizontal surface by the force shown. If the coefficient of kinetic friction between the block and the surface is 0.30, F = 20 N, $\theta$ = 30 $\degree$ , and M = 3.0 kg, what is the magnitude of the acceleration of the block?

A)2.8 m/s2
B)2.3 m/s2
C)1.8 m/s2
D)3.3 m/s2
E)5.4 m/s2

Question 39

A 1.8-kg block is released from rest at the top of a rough 30 $\degree$ inclined plane. As the block slides down the incline, its acceleration is 3.0 m/s2 down the incline. Determine the magnitude of the force of friction acting on the block.

A)4.2 N
B)3.0 N
C)3.4 N
D)3.8 N
E)2.3 N

Question 40

A 3.0-kg block slides on a rough horizontal surface. A force of 8.0 N acting parallel to the surface is applied to the block. The coefficient of kinetic friction between the block and the surface is 0.15. What is the magnitude of the block's acceleration?

A)1.9 m/s2
B)1.2 m/s2
C)2.3 m/s2
D)1.5 m/s2
E)2.9 m/s2

Question 41

An aircraft pilot experiences weightlessness as she passes over the top of a loop-the-loop manoeuvre. If her speed is 200 m/s at the time, find the radius of the loop.

Question 42

An object is on the flat bed of a truck that is accelerating along a straight horizontal road. The coefficient of static friction is 0.300 in this case. Of the following choices, which is the lowest value of acceleration that would result in the object sliding on the bed of the truck?

A)0.280 m/s2
B)0.310 m/s2
C)2.93 m/s2
D)2.99 m/s2
E)3.02 m/s2

Question 43

A space station in the form of a large wheel, 120 m in diameter, rotates to provide an 'artificial gravity' of 3.00 m/s2 for persons located at the outer rim. Find the rotational frequency of the wheel (in revolutions per minute) that will produce this effect.

Question 44

At Bathurst, a race car starts from rest on a circular track of radius 400 m. Its speed increases at the constant rate of 0.500 m/s2. At the point where the magnitudes of the radial and tangential accelerations are equal, determine (a) the speed of the race car, and (b) the elapsed time.

Question 45

A sample of blood is placed into a centrifuge of radius 15.0 cm. The mass of a red corpuscle is 3.0 *10-16 kg, and the centripetal force required to make it settle out of the plasma is 4.0 * 10-11 N. At how many revolutions per second should the centrifuge be operated?

Question 46

An extremely drunk physics student, while on holiday in the Snowy Mountains, decides to snowboard down a hill on a bathroom scale (don't ask us why …). The student has a mass of 60 kg, the bathroom scale has a mass of 3 kg and the icy hill a slope of 20°. Assume there is no frictional force between the bottom of the scale and the hill. The static friction force the scale exerts on the person is:

A)0 N.
B)201 N.
C)211 N.
D)553 N.
E)580 N.

Question 47

A box is dropped onto a conveyor belt moving at 2 m/s. If the coefficient of friction between the box and the belt is 0.3, how long before the box moves without slipping?