Deck 5: Applications of Newtons Laws

Question 1

A block of mass m is at rest on an inclined plane that makes an angle of 30º with the horizontal,as shown in the figure.Which of the following statements about the force of static friction is true?

A)f_s > mg
B)f_s > mg cos 30º
C)f_s = mg cos 30º
D)f_s = mg sin 30º
E)None of these statements is true.

Answer 1

f_s = mg sin 30º

Question 2

A worker pulls horizontally on a rope that is attached to a 10-kg crate resting on a rough floor.The coefficients of static and kinetic friction are 0.5 and 0.3,respectively.The worker pulls with a force of 40 N.The frictional force exerted by the surface is

A)30 N
B)50 N
C)10 N
D)100 N
E)40 N

Answer 2

40 N

Question 3

Two objects are sliding at the same speed across a wooden surface.The coefficient of kinetic friction between the first object and the surface is twice that between the second object and the surface.The distance traveled by the first object before it stops is S.The distance traveled by the second object is

A)impossible to determine without knowing the masses involved.
B)2S
C)S/2
D)S
E)4S

Answer 3

2S

Question 4

A mass m is placed on a rough incline at an angle $\theta$ to the horizon.A force F is applied up the incline,to prevent the mass from sliding down the incline,and it is just enough to prevent the mass from sliding down the incline.Using the compass rose,the direction of the frictional force is along

A)(a)
B)(b)
C)(c)
D)(d)
E)(e)

Question 5

A tired worker pushes a heavy (100-kg)crate that is resting on a thick pile carpet.The coefficients of static and kinetic friction are 0.6 and 0.4,respectively.The worker pushes with a force of 500 N.The frictional force exerted by the surface is

A)1000 N
B)600 N
C)500 N
D)400 N
E)100 N

Question 6

A block of wood is pulled by a horizontal string across a rough surface at a constant velocity with a force of 20 N.The coefficient of kinetic friction between the surfaces is 0.3.The force of friction is

A)impossible to determine without knowing the mass of the block.
B)impossible to determine without knowing the speed of the block.
C)0.3 N
D)6 N
E)20 N

Question 7

An object with a mass of 5.5 kg is allowed to slide from rest down an inclined plane.The plane makes an angle of 30º with the horizontal and is 72 m long.The coefficient of friction between the plane and the object is 0.35.The speed of the object at the bottom of the plane is

A)5.3 m/s
B)15 m/s
C)24 m/s
D)17 m/s
E)11 m/s

Question 8

A mass M = 5.6 kg on a horizontal table is pulled by a horizontal string that passes over a frictionless pulley to a free-hanging mass m = 3.4 kg.The coefficient of friction between M and the table is 0.28.The acceleration of M is

A)3.7 m/s²
B)2.0 m/s²
C)2.2 m/s²
D)0.20 m/s²
E)0.49 m/s²

Question 9

A heavy truck and a light car are traveling at the same speed on the same roadway.If the coefficients of static friction between their tires and the road are the same,which vehicle will be able to stop in the shortest distance? Assume both have the same braking force.

A)the car
B)the truck
C)Both will be able to stop in the same distance.
D)One cannot tell without knowing their coefficients of kinetic friction.
E)One cannot tell without knowing their masses.

Question 10

Which of the following statements is NOT true about friction?

A)µ_k is less than µ_s
B)µ_k is independent of the relative speed of the surfaces in the range of about 1 cm/s to several meters per second.
C)µ_k depends on the relative speed of the surfaces at speeds over several meters per second.
D)The coefficients of friction depend on the nature of the surfaces.
E)The force of static friction depends on the area of contact between the two surfaces.

Question 11

An Atomic Force Microscope consists of a cantilever with a very fine tip on one end.The lever is driven by a piezoelectric motor allowing the tip to scan a surface on an atomic scale.As it scans the surface what is the main frictional force between the tip and the surface?

A)static
B)kinetic
C)rolling
D)all three
E)there is no frictional force

Question 12

Which fundamental force(s)gives rise to friction?

A)gravitational force
B)electromagnetic force
C)weak nuclear force
D)strong nuclear force
E)(A)and (B)

Question 13

A mass m is placed on a rough incline at an angle $\theta$ to the horizon.A force F is applied up the incline so that the mass slides up the incline.Using the compass rose,the direction of the frictional force is along

A)(a)
B)(b)
C)(c)
D)(d)
E)(e)

Question 14

A 100-kg block is pushed up a 30º incline that is 10 m long.If the coefficient of friction between the block and the incline is 0.1,the constant force parallel to the incline that is required to move the block from rest at the bottom of the incline to the top in 3 s is approximately

A)0.49 kN
B)0.085 kN
C)0.22 kN
D)0.80 kN
E)0.58 kN

Question 15

An object with a mass M = 250 g is at rest on a plane that makes an angle $\theta$ = 30º above the horizontal.The coefficient of kinetic friction between M and the plane is µ_k = 0.100.Mass M is attached by a string to another mass, m = 200 g,which hangs freely.When mass m has fallen 30.0 cm,its speed is

A)83 cm/s
B)48 cm/s
C)160 cm/s
D)59 cm/s
E)72 cm/s

Question 16

The SI units for the coefficient of friction are

A)newtons per meter.
B)meters.
C)newtons.
D)newtons times meters.
E)None of these is correct; the coefficient of friction has no units.

Question 17

A block is placed on a plane whose angle of inclination is 30º.The coefficients of static and kinetic friction for the block on the inclined plane are both 0.2.The block

A)remains stationary on the inclined plane.
B)accelerates down the inclined plane.
C)travels down the inclined plane at constant velocity.
D)travels up the inclined plane at constant velocity.
E)accelerates up the inclined plane.

Question 18

Four identical blocks are moving on a surface for which the coefficient of kinetic friction between each block and the surface is µ_k.The velocity of each block is indicated by the vector on the block.For which block is the force of friction between the surface and the block greatest?

A)1
B)2
C)3
D)4
E)The force of friction is the same for all blocks.

Question 19

A block of mass m is pulled in the direction shown in the figure across a rough surface at a constant velocity.The magnitude of the frictional force is

A)µ_kmg
B)µ_kT cos $\theta$
C)µ_k(T - mg)
D)µ_kT sin $\theta$
E)µ_k(mg - T sin $\theta$ )

Question 20

A 50-kg block rests on a horizontal surface.The coefficient of static friction $\mu$ _a = 0.50.The coefficient of kinetic friction $\mu$ _k = 0.35.A force of 250 N is applied as shown.

A)The block remains at rest.
B)The block moves and continues to move at constant velocity.
C)The block accelerates to the right.
D)The block does not move until is increased to greater than 490 N.
E)No conclusions can be drawn concerning the movement of the block from the information given.

Question 21

A block of mass m_b rests on a horizontal surface and is accelerated by means of a horizontal cord that passes over a frictionless peg to a hanging weight of mass m_w.The coefficient of kinetic friction between the block and the horizontal surface is µ and the tension in the cord is T.The acceleration of the block is given by

A)(T - m_wg)/(m_w + m_b)
B)T/(µm_bg + m_b)
C)(T - µm_b)/m_b
D)(m_wg - T)/m_w
E)T/m_b - µm_bg

Question 22

A block of mass m is pulled in the direction shown in the figure across a rough surface with a constant acceleration .The magnitude of the frictional force is

A)µ_kmg
B)T cos $\theta$ - ma
C)µ_k(T - mg)
D)µ_kT sin $\theta$
E)µ_k(mg + sin $\theta$ )

Question 23

The system in the figure is moving with constant speed v to the right on a stationary ramp.The system will accelerate to the right if

A)angle $\beta$ is increased.
B)angle $\alpha$ is increased.
C)coefficient of friction µ_k for surface A is increased.
D)coefficient of friction µ_k for surface B is increased.
E)normal force on block 2 is increased.

Question 24

The blocks shown in the figures have equal masses and are made of the same material.The velocity is the same in each figure.The total frictional force exerted by the surface on the blocks is

A)greater in Figure C than in Figure A or Figure B.
B)the same in Figure C as in Figure A.
C)the same in Figures A,B,and C.
D)the same in Figure A and Figure B.
E)the same in Figure C and Figure B.

Question 25

The net force acting on an object is zero.You can therefore definitely conclude that the object is

A)at rest.
B)moving in a straight line at constant speed.
C)moving in a circle at constant speed.
D)undergoing acceleration.
E)either at rest or moving in a straight line at constant speed.

Question 26

A horizontal force acts on a mass m that lies on a horizontal surface.The acceleration of m is .The coefficient of kinetic friction µ_k between mass m and the surface can be calculated from

A)µ_k = a/g
B)µ_k = (F/mg)- (a/g)
C)µ_k = (F/mg)+ (a/g)
D)µ_k = 0
E)None of these is correct.

Question 27

A 6000-kg truck is accelerating at 0.5 m/s² up a slope of 5 degrees.If the opposing forces due to road friction and air resistance are 80 N per 1000 kg of truck mass,calculate the driving force needed for the truck to accelerate up the incline.

A)8100 N
B)8600 N
C)8200 N
D)7700 N
E)1700 N

Question 28

If a jet plane doubles the speed,the drag force on the jet plane

A)decreases by hal
B)is unchanged
C)doubled
D)quadrupled
E)depends how many passengers the plane is carrying

Question 29

An object with a mass of m = 12.0 g is falling through a resistive fluid in which g is constant.The retarding frictional force due to the fluid is F = bv,where F is the force in newtons,b is a constant,and v is the speed in meters per second.If F = 3.2 $\times$ 10^-2 N when v = 16.0 m/s,the terminal speed of the object falling through the fluid is

A)0.12 m/s
B)59 m/s
C)0.19 km/s
D)16.0 m/s
E)None of these is correct.

Question 30

In drag racing,the driver deploys a parachute at the end of the mile run.The parachute works well because

A)the dragster does not have any brakes to save weight.
B)the drag force due to the parachute is large at high speeds.
C)there is no rolling friction at high speeds.
D)the driver has no time to apply the brakes.
E)the deployment of the parachute is part of the show.

Question 31

A horizontal force is used to push an object of mass m up an inclined plane.The angle between the plane and the horizontal is $\theta$ .The normal reaction force of the plane acting on the mass m is

A)mg cos $\theta$ + F cos $\theta$
B)mg cos $\theta$
C)mg cos $\theta$ + F sin $\theta$
D)mg cos $\theta$ - F cos $\theta$
E)impossible to determine because the coefficient of friction is not given.

Question 32

A box (m = 20 kg)is sitting on a horizontal surface.It is connected to a massless hook by a light string passing over a massless pulley wheel.The coefficients of friction between the box and the surface are 0.50 (static)and 0.30 (kinetic).On top of m is a second box M of mass 20 kg.The coefficients of friction between the boxes m and M are 0.80 (static)and 0.60 (kinetic).How much weight needs to be added to the hook until the box just begins to move.

A)10 kg
B)98 kg
C)20 kg
D)16 kg
E)200 kg

Question 33

A block of mass M is sliding down a rough inclined surface that makes an angle $\theta$ with respect to the horizontal.If the coefficient of static friction is $\mu$ _s and kinetic friction $\mu$ _k,then the acceleration of the block down the incline is equal to:

A)gsin $\theta$ - g $\mu$ _s $\times$ cos $\theta$
B)gcos $\theta$ - g $\mu$ _k $\times$ cos $\theta$
C)g $\mu$ _s $\times$ cos $\theta$ - gsin $\theta$
D)gsin $\theta$ - g $\mu$ _k $\times$ cos $\theta$
E)gsin $\theta$ - g $\mu$ _s $\times$ cos $\theta$ - g $\mu$ _k $\times$ cos $\theta$

Question 34

A box (M = 20 kg)is sitting on a horizontal surface.It is connected to a massless hook by a light string passing over a massless pulley wheel.The coefficients of friction between the box and the surface are 0.80 (static)and 0.30 (kinetic).If 15 kg (in total)are placed on the hook,calculate the acceleration of the box.

A)10 m/s
B)4.4 m/s
C)2.5 m/s
D)12 m/s
E)0

Question 35

A mass m₂ = 1.5 kg rests on a horizontal table.The coefficients of friction between m₂ and the table are µ_s = 0.3 and µ_k = 0.25.The mass m₂ is attached by strings to masses m₁ = 2.5 kg and m₃ = 4.5 kg as shown.Masses m₁ and m₃ hang freely.The system is initially held at rest.After it is released,the acceleration of m₂ is approximately

A)1.9 m/s²
B)2.4 m/s²
C)3.0 m/s²
D)zero
E)13 m/s²

Question 36

In the equation F = bv,F is the force on an object that is moving in a viscous medium,b is a constant,and v is the speed of the falling object.The SI units of the constant b are

A)m/s
B)kg · s
C)kg/s
D)kg · m
E)m/s²

Question 37

As a sky diver falls through the air,her terminal speed

A)depends on her mass.
B)depends on her body's orientation.
C)depends on the local value of the acceleration due to gravity.
D)depends on the density of the air.
E)is described by all of the above.

Question 38

A 2-kg block sits on an incline where the top part of the incline has a coefficient of kinetic friction ( $\mu$ _k)of 0.70.The bottom section of the plane has $\mu$ _k = 0.95.The angle of inclination is 40 degrees.The block is released and travels 10 m along the initial part of the incline and then enters the lower section.Calculate how far the block travels along the second section before it is brought to a stop.

A)2.7 m
B)21 m
C)23 m
D)13 m
E)260 m

Question 39

A 50-kg box is placed in the bed of a truck.The coefficient of friction between the box and the truck bed is 0.54.If the truck is traveling at 87 km/h (~54 mph)then calculate the minimum distance the truck can stop in without the box sliding into the cab.

A)99 m
B)1.4 $\times$ 10³ m
C)55 m
D)1.2 $\times$ 10² m
E)2.8 $\times$ 10² m

Question 40

A block with a mass of 10 kg is at rest on a horizontal surface.The coefficient of static friction between the block and the surface is 0.30,and the coefficient of kinetic friction is 0.25.A force of 20 N acts on the block toward the left.The magnitude of the frictional force on the block is

A)10 N
B)20 N
C)0.10 kN
D)30 N
E)3.0 N

Question 41

A car going around a curve of radius R at a speed V experiences a centripetal acceleration a_c.What is its acceleration if it goes around a curve of radius 3R at a speed of 2V?

A)(2/3)a_c
B)(4/3)a_c
C)(2/9)a_c
D)(9/2)a_c
E)(3/2)a_c

Question 42

The figure shows a piece of sheet metal suspended in two positions by a string.From the way the metal hangs,you can see that the center of gravity is nearest point

A)1
B)2
C)3
D)4
E)5

Question 43

An L-shaped piece,represented by the shaded area on the figure,is cut from a metal plate of uniform thickness.The point that corresponds to the center of mass of the L-shaped piece is

A)1
B)2
C)3
D)4
E)5

Question 44

The shaded area in the figure represents a uniformly thick sheet of metal.The center of mass of the sheet is closest to point

A)1
B)2
C)3
D)4
E)5

Question 45

An object traveling in a circle at constant speed

A)is moving with constant velocity.
B)may be slowing down or picking up speed.
C)experiences no acceleration.
D)experiences an acceleration toward the center of the circle.
E)is described by none of the above statements.

Question 46

A proud new Jaguar owner drives her car at a speed of 25 m/s into a corner.The coefficients of friction between the road and the tires are 0.70 (static)and 0.40 (kinetic).What is the minimum radius of curvature for the corner in order for the car not to skid?

A)3.5 $\times$ 10² m
B)64 m
C)2.1 $\times$ 10² m
D)1.6 $\times$ 10² m
E)91 m

Question 47

A particle is moving uniformly in a circle with radius 50 cm.The linear speed of the particle is 60 cm/s.The acceleration of the particle has a magnitude of

A)zero
B)36 m/s²
C)1.8 $\times$ 10⁵ cm/s²
D)72 cm/s²
E)3.6 m/s²

Question 48

When you accelerate your car,the front of the car lifts up slightly.Or when you brake,the front dips down.The primary reason is because the

A)center of mass of the car and its contents is below the center of the wheel.
B)center of mass of the car and its contents is above the center of the wheel.
C)center of mass of the car and its contents is at the center of the wheel.
D)center of mass of the car and its contents is above the road.
E)car has inertia.

Question 49

A particle moving with uniform Motion Along a Curved Path has a period of 0.24 s and a speed of 4.2 m/s.The radius of the path of the particle is

A)16 cm
B)2.6 cm
C)1.0 m
D)0.062 cm
E)1.4 cm

Question 50

The center of mass of the system of particles shown in the diagram is at point

A)1
B)2
C)3
D)4
E)5

Question 51

A ball of mass m is attached to a thin string and whirled in a vertical circle or radius r.The tension in the string at point e where the ball is moving with speed v is

A)mg
B)mg - mv²/r
C)mg + mv²/r
D)mv²/r
E)none of the above.

Question 52

A barbell is 1.5 m long.Three weights,each of mass 20 kg,are hung on the left and two weights of the same mass,on the right.The width of each weight is 4 cm and each group of weights is placed 4 cm from the ends.Where is the center of mass of the barbell as measured from the mid-point,M,of the bar? The bar is of uniform mass and has mass 5 kg,and the retaining collars are of negligible mass.Take to the right as positive.

A)-5.90 cm
B)-5.62 cm
C)+5.62 cm
D)+5.90 cm
E)None of the above

Question 53

The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path.The speed of the ball is constant.If the string should break at the instant shown,the path that the ball would follow is

A)1
B)2
C)3
D)4
E)impossible to tell from the given information.

Question 54

A block slides down a frictionless incline.The path at the bottom of the incline is an arc of a circle.The direction of the net force on the block at the bottom of the arc (point P)is along (use the compass rose)

A)(a)
B)(b)
C)(c)
D)(d)
E)(e)

Question 55

The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path.Assume that air resistance is negligible.The free-body diagram that best represents the net force acting on the ball is

A)1
B)2
C)3
D)4
E)5

Question 56

A professor likes to demonstrate centripetal force by swinging a bucket of water in the vertical direction.What is the minimum speed he must swing the bucket at the top of the circle if he is not to get drenched? (Assume that his arm is 1 m long.)

A)1.1 m/s
B)2.1 m/s
C)3.1 m/s
D)4.1 m/s
E)5.1 m/s

Question 57

When a particle moves in a circle with constant speed,its acceleration is

A)constantly increasing.
B)constant in direction.
C)zero.
D)constant in magnitude.
E)constant in magnitude and direction.

Question 58

The mass of the rectangle in the figure is M,the mass of the ring is M,and the mass of the circle is 3M.The center of mass of the system with respect to the origin O is located at point

A)1
B)2
C)3
D)4
E)5

Question 59

The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path.Assume that air resistance is negligible.The free-body diagram that best represents the acceleration of the ball is

A)1
B)2
C)3
D)4
E)5

Question 60

A car experiences both a centripetal and a tangential acceleration.For which of the following would this be true?

A)It is going around a curve at a constant speed.
B)It is going around a curve and slowing down.
C)It is going along a straight road at a constant speed.
D)It is going along a straight road and increasing its speed.
E)It is going along a straight road and decreasing its speed.

Question 61

Three smiley faces are situated along the x axis as follows: m₁ = 5 kg at 3.0 m,m₂ = 3 kg at 6.0 m and m₃ = 2 kg at 8.0 m.Where is the center of mass situated?

A)3.9 m
B)4.9 m
C)5.5 m
D)4.1 m
E)5.1 m

Question 62

Four smiley faces are situated along the x axis as follows: m₁ = 5 kg at 0.0 m,m₂ = 3 kg at 4.0 m,m₃ = 3 kg at x m,and m₄ = 2 kg at 8.0 m.If the center of mass is situated at 3.54 m,where is m₃ located?

A)3.5 m
B)7.0 m
C)6.0 m
D)4.0 m
E)5.0 m

Question 63

A boy is standing at the stern (back)of a boat that is 8.0 m long.There is no friction between the boat and the water.The boy has a mass of 63 kg and the boat has a mass of 780 kg.The bow (front)of the boat is touching a dock and the fore-and-aft axis of the boat is perpendicular to the dock.The boy walks from the stern of the boat to the bow.When he reaches the bow,his distance from the dock is

A)7.6 m
B)0.65 m
C)0.51 m
D)0.56 m
E)1.3 m

Question 64

A car of mass 3.0 $\times$ 10³ kg traveling at a speed of 20 is passing a truck of mass 7.5 $\times$ 10³ kg traveling at a speed of 16 in the same direction.What is the speed of the center of mass of this system?

A)16
B)17
C)18
D)19
E)20

Question 65

Use the figure below for the problem. A mass, m₁, attached to a spring is placed on a cart with mass m₂, which moves freely and without friction on a table. m₁ slides without friction on the cart and is ¼ the mass of m₂.
When m₁ moves with a displacement of 1 cm in the +x direction,what is the displacement of m₂?

A)m₂ does not move
B)m₂ moves cm in the +x direction
C)m₂ moves 1 cm in the +x direction
D)m₂ moves cm in the -x direction
E)m₂ moves 1 cm in the -x direction

Question 66

A 1.0-kg mass is acted on by a net force of 4.0 N and a 3.0-kg mass is acted on by a net force of 3.0 N,in the directions shown.The acceleration of the center of mass of this system is approximately

A)1.3 m/s²,53º N of E
B)1.8 m/s²,45º N of E
C)4.0 m/s²,due north
D)5.0 m/s²,N of E
E)7.0 m/s²,53º N of E

Question 67

The picture on the right shows an exploding firework high up in the air,just after the firework has come to a rest.Which point best describe the center of mass of the explosion? Picture by H.K.Ng

A)a
B)b
C)c
D)d
E)e

Question 68

Three particles having a total mass of 6 kg are subjected to three forces,as shown in the figure.The magnitude of one force is presented to furnish the scale factor for the others.What is the acceleration of the center of mass of the system?

A)It is knowable only if the mass of each particle is given.
B)6.6 m/s²
C)zero
D)-2 m/s²
E)-2 m/s²

Question 69

Use the figure below for the problem. A mass, m₁, attached to a spring is placed on a cart with mass m₂, which moves freely and without friction on a table. m₁ slides without friction on the cart and is ¼ the mass of m₂.
When m₁ is allowed to oscillate along m₂,what is the motion of m₂?

A)m₂ does not move
B)m₂ moves in the same direction as m₁
C)m₂ moves in the opposite direction of m₁
D)Depends on the spring constant
E)None of the above

Question 70

A uniform horizontal bar is in a region of space where the acceleration due to gravity g varies,increasing from left to right.Where is the location of the center of mass relative to the center of gravity?

A)They are at the same location.
B)The center of mass is to the left of the center of gravity.
C)The center of gravity is to the left of the center of mass.
D)It depends on the shape of the bar.
E)It depends on how much g changes.

Question 71

In the figure,m₁ = 3 kg,m₂ = 8 kg,and m₃ = 4 kg.The forces are ₁ = 1 N + 1 N , ₂ = 1 N + 1 N ,and ₃ = -2 N .The acceleration of the center of mass is approximately

A)0.13 m/s²
B)0.13 m/s² at an angle of 45º with the x axis
C)0.13 m/s²
D)0.27 m/s² at an angle of 45º with the x axis
E)0.27 m/s²

Question 72

The Earth has mass 5.89 $\times$ 10²⁴ kg.The moon has mass 7.36 $\times$ 10²² kg and is 3.84 $\times$ 10⁵ km from Earth.How far from the center of Earth is the center of mass of the Earth-moon system?

A)4.7 $\times$ 10³ km
B)7.4 $\times$ 10³ km
C)1.9 $\times$ 10⁵ km
D)2.1 $\times$ 10⁵ km
E)3.8 $\times$ 10³ km

Question 73

Four smiley faces are situated along the x axis as follows: m₁ = 5 kg at -5.0 m,m₂ = 3 kg at -2.0 m,m₃ = 3 kg at 1.0 m,and m₄ = 2 kg at 3.0 m.Where is the center of mass situated?

A)3.1 m
B)0.0 m
C)-1.7 m
D)-0.80 m
E)-3.1 m