Physics 114 Final Exam

Consider the angular velocity-versus-time graph in Figure P7.62 in the problems section at the end of chapter 7. What is the angular acceleration of the object between t = 0 s and t = 2 s?

-100 rad/s^2

Can you always apply Hooke's Law to a spring?

No

Object A has a mass mm and a speed v, object B has a mass m/2 and a speed 4v, and object C has a mass 3m and a speed v/3. Rank the objects according to the magnitude of their momentum.

Smallest momentum: Object A and Object C Largest momentum: Object B

If a metal wire is 4m long and a force of 5000N causes it to stretch by 1mm, what is the strain?

Strain=(deltaL/L) deltaL=change in length L=original length S=0.001/4=0.00025 The strain is the fractional change in length. It is the ratio of the change in length to its original length.

Balls are attached to light rods and can move in horizontal circles as shown in Figure P7.19 in the problems section at the end of chapter 7. Rank the torque applied to the balls about the center of the circle, from largest to smallest.

T4>T3=T2>T1

Which of the following is true?

The center of gravity tends to lie closer to the heavier objects or particles that make up the entire object.

If you kick a ball, you apply an impulse. The impulse is equal to

The change in momentum of the ball.

The drag force pushes opposite your motion as you ride a bicycle. If you double your speed, what happens to the magnitude of the drag force?

The drag force goes up by a factor of 4.

In general, the spring force always points _________________ the displacement from equilibrium.

in the opposite direction from

If you are performing the weightlifting exercise known as the strict curl, the tension in your biceps tendon is __________.

larger than the weight you are lifting

Springs can stretch; so can different materials, including

Glass, Steel, Rubber

What is the moment of inertia of a 1.5-kg-rod that rotates about its center? The length of the rod is 1.8 m.

I=1/12mL^2 =1/12(1.5)(1.8)^2 I=0.410 kg* m^2

A football of mass 0.430 kg is initially at rest. After being kicked, the football moves with a speed of 5.00 m/s. What was the magnitude of the impulse applied to the football?

J=deltap=pfinal-pinitial pfinal=mfinalvfinal pinitial=minitialvinitial pfinal=(0.430)(5)=2.15 pinitial(0.430)(0)=0 J=deltap=2.15-0=2.15 2.15 kg* m/s

A 1700kg rhino charges at a speed of 50.0km/h What is the magnitude of the average force needed to bring the rhino to a stop in 0.50s? Express your answer to two significant figures.

J=faverage*deltat J=deltap deltap=pfinal-pinitial pfinal=(1700)(0)=0 pinitial=(1700)(50,000 m/3600s)=23611.1 deltap=0-23611.1=-23611.1 J=-23611.1=faverage*0.50 faverage=-23611/0.50 faverage=-4.7*10^4 N Magnitude=absolute value=4.7*10^4 N

A 3.6 kg chihuahua charges at a speed of 3.3m/s. What is the magnitude of the average force needed to bring the chihuahua to a stop in 0.50s? Express your answer to two significant figures.

J=faverage*deltat J=deltap=pfinal-pinitial pfinal=(3.6)(0)=0 pinitial=(3.6)(3.3)=11.88 pfinal-pinitial=-11.88 J=deltap=-11.88 -11.88=faverage*0.50 -11.88/0.50=faverage faverage=-24 N Magnitude=absolute value=24 N

The Young's modulus of aluminum is 69GPa, of nylon is 3GPa, of tungsten is 400GPa, and of copper is 117GPa. If equal-size samples were put under equivalent tensile stresses, how would you rank the materials by the degree to which they would be elongated?

(least) Tungsten < Copper < Aluminum < Nylon (most) Materials that have a high Young's modulus are difficult to stretch.

In the opening scenes of the prelecture video, we outlined some of the key properties of momentum. Which of the following statements are consistent with these properties?

1. An object's momentum is equal to the product of its mass and its velocity. 2. Momentum is a vector quantity. The momentum of an object is a vector quantity, and is defined as the product of the object's mass and its velocity.

The ability of a force to cause a rotation depends on:

1. The magnitude of the force. 2. The distance r from the pivot - the axis about which the object can rotate - to the point where the force is applied. 3.The angle at which the force is applied.

The drag force:

1. increases in magnitude as the object's speed increases 2. is opposite in direction to the velocity of the object v⃗→

Generally, the ______ in a ______ string or rope ______ the magnitude of the ______ pulling on the end of the string or rope.

1. tension 2. massless 3. equals 4. force

Consider Example 8.3. About the pivot point at the left end of the board:

1. the torque applied by the scale force is positive. 2. the torque applied by the weight force of the person is negative. 3. the torque applied by the weight force of the board is negative

How many radians are equivalent to 150°? Give your answer to two signficant figures.

150*(2pi/360)=2.6 radians

At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 1.0 m/s?

1500(1.0)=100(x) 1500/100 x=15 m/s

Suppose a child swings around her straight arm counterclockwise about her shoulder joint. If her arm is 40.0 cm long, and her arm completes exactly 2 revolutions in 0.95 s, what is her arm's angular velocity in rad/s?

2 revolutions=2*360=720 degrees(2pi/360)=12.57 radians w=angle/time w=12.57/0.95=13.2 rad/s

A spring has a equilibrium length of 0.100 m. When a force of 40.0 N is applied to the spring, the spring has a length of 0.140 m. What is the value of the spring constant of this spring?

40.0 N=k(0.140-0.100) 40.0/0.04=k k=1000 N/m

A metal bar is elongated by 2mm when put under a certain amount of tension. How much will it be elongated if the tension is doubled?

4mm Because the area will usually not change by a noticeable amount, an increase in tension will lead to a proportional increase in stress and, therefore, a proportional increase in strain.

Consider the angular position-versus-time graph in Figure P7.9 in the problems section at the end of chapter 7. What is the angular velocity of the object between t = 0 s and t = 10 s?

5 radians

Two boxes are suspended from a rope over a pulley. Each box has weight 50 N. What is the tension in the rope?

50 N

Shown below is a graph of a force applied to a small object as a function of time. If the object has a mass of 5.0kg and is at rest a t=0s, how fast is the object moving at t=4.0s?

7.2 m/s Impulse(J) equals area under the curve at 4 secs (4*4)+1/2((12)(4 seconds)=24 24=deltap=m(vfinal-vinitial) 24=deltap=5(vfinal-0) 24/5=vfinal vfinal=

For the climber in Figure 8.5, where does the author recommend choosing the pivot point?

At the point where the climber's feet touch the wall.

In the video, we looked at the problem of balancing a pencil on your fingertip, which is easy for a long pencil, hard for a short pencil. If you consider a long and a short pencil tipped to the side, the __________ of the shorter pencil is larger.

Angular acceleration; angular acceleration is inversely proportional to moment of inertia(resistance to torque force)

In the video, the two stuffed animals that rode on the turntable had the same __________ but had different _________

Angular velocity Velocity

Ball A with diameter d and ball B with diameter 2d are dropped from the same height. When the two balls have the same speed, what is the ratio of the drag force on ball A to the drag force on ball B?

Ball A=1/2CdpAv^2 Ball B=1/2CdpAv^2 Ratio Ball A to Ball B: 1/2Cdp(d)v^2/(pv((2d)^2)/n)=1/2*1/2=0.250

What is the answer to the "Stop to Think 7.6" question?

D>A>C>B

The impulse imparted on an object is:

Equal to the area under the applied force vs time curve.

Which of the following forces in Figure 7.16 is the most effective at opening the door?

F1; greater moment arm

A particle in uniform circular motion has a period of 4.0 seconds. What is the particle's frequency?

F=1/T F=1/4 F=0.250 s^-1

What is the net force acting on a particle with mass m moving with uniform speed of v in a circular path with radius r?

F=ma F=m(v^2/r) F=mv^2/r

The maximum stress a bone can experience before it fractures is around 108N/m2108N/m2 . How much stress could the bone experience if it were twice as large in diameter?

The maximum stress would be no different. The strength of a material is measured in terms of maximum stress, not force. Therefore, larger objects can withstand larger tensile forces because stress is inversely proportional to area.

For an object to be in static equilibrium, the net force must be equal to zero and

The net torque must be equal to zero.

Which of the following is true?

The net torque on an object in static equilbrium is zero when calculated about any pivot point.

When we draw a diagram of the forces acting on an extended object, the tail of the force vector for the weight should be at

The object's center of gravity.

For an object in uniform circular motion, what can you say about the directions of the velocity, acceleration, and net force vectors?

The velocity vector is perpendicular to the acceleration vector; the acceleration vector is parallel to the net force vector.

In the video, a car rounding a corner and a car going over the crest of a hill are both presented as examples of...

Uniform circular motion

A very rigid material—one that stretches or compresses only slightly under large forces—has a large value of __________.

Young's modulus

Momentum is

a vector quantity

Consider Example 8.12. Which of the following forces has the largest magnitude?

force by bicep tendon

A 2.00-m long rod is acted on by two forces, F1 and F2 (see Figure P7.23 in the problems section at the end of chapter 7). F2 acts at a point 0.500 m from the left end. F2 has a magnitude of 25.0 N and F1 has a magnitude of 20.0 N. The rod can rotate or pivot about its center. a. If we set the pivot to be at the center of the rod, what is the value of r⊥ for F2? b. About the center of the rod, what is the magnitude of the torque applied by F2? Note that the magnitude of the torque is given as: τ=r⊥F c. How much of the force F1 is perpendicular to the rod? d. About the center of the rod, what is the magnitude of the torque applied by F1? Note that the magnitude of the torque is given as: τ=r⊥F

a. 0.500 m b. t=0.500(25)=12.5 N*m c. F=20 N(cos(45)=14 N d. t=(1.0)(14)=14 N (distance from center to the force)

Two boxes of mass 6.0 kg and 3.0 kg are pushed across a smooth (frictionless) floor by a 18 N force that is horizontal to the floor. a. How many forces are exerted on Box A? b. How many forces are exerted on box B? c. Suppose we consider the two boxes as a single box, box C that has a mass of 9.0 kg. What is the net force on box C? d. What is the acceleration of box C? e. Rank the magnitudes of the accelerations of boxes A, B and C. f. If all the boxes have the same acceleration, what is the magnitude of the force that box A exerts on box B? g. What is the magnitude of the force that box B exerts on box A?

a. 4 forces b. 3 forces c. 18 N d. 18/9=2.0 m/s^2 e. A=B=C f. 18 N-(6.0 kg)(2.0 m/s^2)=6.0 N g. (3.0 kg)(2.0 m/s^2)

A particle moves in a circle with radius 10 cm and with a uniform speed 1.3 m/s. What is the centripetal acceleration of this particle?

a=(v^2/r)=[(1.3)^2/0.1]=17.0 m/s^2

Suppose a child starts swinging around her straight arm counterclockwise about her shoulder joint, starting at rest. If her arm's angular speed reaches 13 rad/s in 1.5 seconds, what is her arm's angular acceleration in rad/s2?

a=w/t a=13/1.5 a=8.7 rad/s^2

Very small organisms, like paramecia or protozoa, moving around in water __________.

almost immediately come to rest once they stop swimming

According to the convention used in the textbook, the angular position θ is positive when measured:

counterclockwise from the positive x-axis.

What is the answer to the "Stop to Think 9.3" question?

deltap=pfinal-pinitial pfinal=1 m/s(10 kg) pintial=-2 m/s (10 kg) *going left* deltap=10-(-20)= 30 kg* m/s

A falling object will reach its terminal speed when the magnitude of the drag force is ______________ to the magnitude of the weight force.

equal to

Moment of inertia for rotational motion is the rotational equivalent of:

mass for linear motion

If an object is rotating clockwise, this corresponds to a _____ angular velocity.

negative

Consider Example 8.12. About the elbow joint, according to our convention, what is the sign of the torque applied by the force of the barbell?

negative; clockwise; force of barbell=weight force

The acceleration of a particle that moves with uniform circular motion:

points toward the center of the circle.

Consider Example 8.12. About the elbow joint, according to our convention, what is the sign of the torque applied by the force of the bicep tendon?

positive; counterclockwise

The spring force is ___________________ to the displacement of the end of the spring.

proportional

A force that restores a system to an equilibrium position is called a ____________ force.

restoring

The gravitational _____ can be calculated by assuming that the net force of _____ - that is, the object's weight w⃗→ - acts at a single special point on the object called its __________.

torque gravity center of gravity

Consider Example 8.12. About the elbow joint, according to our convention, what is the sign of the torque applied by the force of the elbow?

torque equals to zero; at pivot (no moment arm)

Suppose a child swings around her straight arm about her shoulder joint at an angular velocity of 13 rad/s. If her arm is 40.0 cm long, what is the speed of her hand?

v=r*w v=(0.4)(13)=5.2 m/s

Which of the following equations correctly equates the net torque on an object to the object's angular acceleration?

τnet=Iα