Name:(4 points)

A

PHYSICS 1050Mid-term Test 1

University of Wyoming15 February 2005

This test is open-note and open-book. This means that any reference material ispermitted during the test. Calculators also are permitted. However, no collaboration,consultation, or communication is allowed by any means, including but not limited toverbal, written, or electronic methods.

If you have a question about the test, please raise your hand. If that does not get theadministrator’s attention, throw something at him. He may try to climb across the desksto hear your question, but he will probably resort to asking you to shout across the room,since once everyone is in their seats, it is really hard to get in or out.

Please do not open this test booklet until everyone has received a booklet and the testadministrator has indicated for you to begin. While you are waiting, make sure that yourname is written at the top of this page. Not only will that get you four easy points, it willsave you the trouble of trying to convince the instructor that some high-scoring test withno name on it is really yours.

Conversion Factors:

12 in = 1 ft3 ft = 1 yd5280 ft = 1 mi

2.54 in = 1 cm39.37 in = 1 m1 lb = 4.5 N

1 day = 24 h1 h = 60 min1 min = 60 s

Physical Constants:

Universal gravitational constantG = 6.67 10 11 Nm2 kg2

gravitational acceleration at earth’ssurface: g = 9.8 m/s2

= 9.8 N/kg

Metric Prefixes:

pico: 10-12

nano: 10-9

micro; 10-6

milli: 10-3

centi: 10-2

kilo: 103

mega: 106

giga: 109

tera: 1012

ANSWER KEY

A page 2 of 12

Multiple choice20 questions, 3 points each.

Please circle the most correct answer from the choices given.

1. Before the Revolution, the French used a unit of length called the toise. The toisewas longer than the meter.If a mountain is exactly 2000 toises high, its height in meters isa. exactly 2000 metersb. less than 2000 metersc. more than 2000 meters

2. The speed limit on Willett Drive by the Arena is 20 miles per hour. How can thisbe converted into the SI units of meters per second?

a. 20 mi h60 min

h

60s

min

5280 ft

mi

12 in

ft

39.37 in

m=…

b. 20 mi

h

5280 ft

mi

12 in

ft

39.37 in

m

60 min

h

60s

min=…

c. 20 mi

h

h

60 min

min

60 s

5280 ft

mi

12 in

ft

m

39.37 in=…

d. 20 mi

h

5280 ft

mi

12 in

ft

m

39.37 in

3600 s

h=…

3. Which of the four vectors illustrated has the largest magnitude?

4. The proper way to add vectors r A and

r B to obtain the vector sum

r A +

r B is shown

in which diagram below?

wrong initial units

in, h don’t cancel

h don’t cancel

A page 3 of 12

5. The graph to the right shows theprogress made by a beetle moving alonga straight line. If the beetle keepsmoving at the same speed, at what timewill it reach the 10-cm mark?a. 4 secondsb. 10 secondsc. 20 secondsd. 25 seconds

6. When a car accelerates uniformly from rest, which quantities increase with time?a. acceleration and velocityb. velocity onlyc. acceleration and distance traveledd. velocity and distance traveled

7. A car driving in the fog rear-ends a stopped semi-trailer. The car stops instantly,and the driver, not wearing his seat belt, impacts the steering wheel. The impact bringshim to a stop in 0.007 s. If the driver’s air bag had deployed, he would have come to astop in 0.025 s. Which of the following statements is true?a. The driver’s change in speed is less with the airbag than without.b. The force on the driver with the airbag is greater than if the airbag were not there.c. The force on the driver with the airbag is less than if the airbag were not there.d. The air bag reduces the driver’s kinetic energy more than the steering wheel alonedoes.

8. Two balls of the same mass and moving with the same velocity collide with awall. Ball A, made of soft clay, sticks to the wall. Ball B, made of rubber, bounces backfrom the wall. Which ball experiences the largest change in momentum before and afterthe collision?a. Ball A.b. Ball B.c. Both have the same change in momentum.d. You can’t tell because you don’t know the time t of the collisions.

No: v is the same

F = v/ tt is different

No: goes from 0.5 mv2 to 0 in both cases.

pAi = mv; pAf = m(0)= 0; pA = mv – 0 = mv

pBi = mv; pBf = m(–v)= –mv; pB = mv – (–mv) = 2mv

A page 4 of 12

9. You are a mechanical engineer hired to design the loop-the-loop roller coaster fora new amusement park. What do you need to consider in your design to keep riders fromfalling out of the coaster at the top of the loop?a. The inward acceleration of the coaster at the top of the loop must be more than g.b. The speed of the coaster must be greater than terminal velocity of free fall.c. Do not allow riders who are too heavy on the coaster.d. The force holding passengers up must exceed the force pulling them down.

10. There is a location between the Earth and the moon, called the Lagrange Point,where the gravitational forces from the Earth and the moon cancel. An object placedexactly at the Lagrange Point will not accelerate toward either the moon or the earth.Since the Earth is more massive than the moon, the Lagrange pointa. is closer to the Moon than to the Earth.b. is exactly midway between the moon and Earth.c. is closer to the earth than to the moon.d. is at a distance that depends on the phase of the moon.

11. A central particle is surrounded by two circularrings of particles, as shown to the right. All the particleshave mass m. What is the direction of the netgravitational force on the central particle due to theparticles in the rings?a. toward the top of the page (up)b. to the rightc. toward the bottom of the page (down)d. to the left

F =Gm1m1r122

Need to get closer tothe moon to equal thepull of gravity from thelarger Earth

A page 5 of 12

12. The diagram to the right shows a person holding a ballstanding at three different places on Earth. If the person dropsthe ball, gravity will make it fall. Which of the diagramsbelow best shows the direction the dropped ball will fall at thethree different positions?

13. My dog weighs 43 pounds. That means that the Earth exerts a gravitational forceof 43 pounds on my dog. The gravitational force my dog exerts on the earth isa. 43 pounds, because of Newton’s third law.b. Less than 43 pounds, because my dog’s gravitational field is much less than theEarth’s.c. Zero, because a dog is too small to have gravity.d. More than 43 pounds, but the Earth is so massive it doesn’t accelerate.

14. The mass of the planet Mars is about 1/10 the mass of Earth, and its radius isabout 1/2 the radius of earth. The weight of the Mars probe Odyssey when it is on thesurface of Mars isa. about 1/10 its weight on Earth.b. more than 1/10 its weight on Earth.c. less than 1/10 its weight on Earth.

Mars’s radius is less than Earth’s, so at the surface you are closer to the

center. if Odyssey were a distance equal to the radius of the Earth from

the center of Mars, its weight would be 1/10 its weight on Earth. Since it is

closer, its weight is more than that.

A page 6 of 12

15.

The diagram above on the left shows a ball on the end of a string being whirled in acircle. The diagram on the right shows the whirling ball as viewed from above. Afterseveral whirls, the string is released when the ball is at Q. Which of these diagramsshows the direction in which the ball will fly, as viewed from above, the instant the stringis released?

16. You are riding in the right side of a car when the driver makes a hard left turn.You feel yourself pressing against the door becausea. you are accelerating outward as the car turns in a curved path.b. the car tilts to the right, so gravity pushes you onto the door.c. the car is accelerating leftward as it turns, pushing into you.d. you are pushing outward on the door, so the door pushes back with an equal andopposite force.

A page 7 of 12

17. Alex is has a flat tire. The guy at the garage, as usual, over-tightened the nutswhen he mounted the tire, so Alex is having trouble loosening them. Which directionshould Alex push on the handle of the lug wrench to get the maximum torque about thenut?

a. straight inwardb. obliquely outwardc. perpendicular to thehandled. obliquely inward

18. The diagram below shows the positions at 1-second intervals of a ball that isthrown upward from (0, 0)at an angle.

0

50

100

0 50 100 150 200 250

Distance (m)

Heig

ht

(m

)

Between the start of the ball’s trajectory at (0, 0) and the end at (0, 240 m),a. the ball’s kinetic energy is constant. That’s total energy.b. the ball’s kinetic energy initially decreases, then passes through zero and increasesagain. Only if the ball has no horizontal speed.c. the ball’s kinetic energy initially decreases, then reaches a minimum value andincreases again.d. the ball’s kinetic energy initially increases, then reaches a maximum value anddecreases again. That’s potential energy.

A page 8 of 12

19. Until he was in his seventies, Henri LaMothe excited circus audiences by belly-flopping from a height of 12 m into 30 cm of water. How can you find what his kineticenergy KE was when he hit the water?a. Estimate his mass m, then use KE =1 2 mv 2 .b. Estimate his mass m, then use KE =work = mgh with h = 12 m.c. Estimate his falling power, then use P = w t w = P t to find the work needed.

d. Solve the equation h = v0 t +1 2 a t( )2 for v.

20. The SI unit for energy is the joule, but power companies usually bill by thekilowatt hour (kWh), which is the energy consumed by applying the power of 1000 wattsfor 1 hour. How can you find how many joules are equal to one kWh?

a.

1000 W

1 h

3600 s

h

J/s

W=L b.

1 h

1000 W

3600 s

h

W

J/s=L

c.

1000 W 1 h3600 s

h

J/s

W=L d.

1000 W 1 h3600 s

h

W s

J=L

Short answer5 questions, 4 points each.

21. The diagram below shows the positions at intervals of 0.05 s of two balls movingfrom left to right. Are either or both of these balls accelerated? Explain.

Both are accelerated, which means that their velocities are not

constant. If their velocities were constant, the spacing between

intervals would be constant, and it is not. Ball A is accelerating to

the right, and ball B is decelerating, or accelerating toward the

left.

1 kWh = 1000 W 1 h, not 1000 W / h or h / 1000 W.

A page 9 of 12

22. A skydiver jumps out of a perfectly good airplane. For a few seconds, sheaccelerates toward the ground, but eventually her velocity reaches a maximum value of“terminal velocity”, so that her falling speed does not change with time.a. Identify two forces that are acting on her body as she falls.

b. In what directions are these two forces acting?

c. What are the relative magnitudes of these two forces before and after she reachesterminal velocity?

23. A feather falls more slowly than a paperweight. Why? (Don’t just identify theforces that are acting on each object; explain why their effects are different for the twodifferent objects.)

gravity pulls downward and air resistance opposes the direction of

her motion.

gravity and air resistance

Before she reached terminal velocity, the pull of gravity was greater than air

resistance, which is why she accelerated. After she reached terminal velocity,

she was not accelerating, so the total force acting on her was zero. This means

that the forces of gravity and air resistance, which were oppositely directed,

had equal magnitudes.

The motion of both objects is governed by their masses and the

forces of gravity and air resistance acting on them. The force of

air resistance is a greater fraction of the feather’s weight than

of the paperweight’s weight. The force of air resistance thus

more effectively acts against the force of the feather’s weight

than the paperweight’s weight.

A page 10 of 12

24. The diagram shows the locations at 1-second intervals of a ball thrown at 50 m/sat an angle of ~53° form horizontal. At each location, draw a vector showing themagnitude and direction of the ball’s acceleration. (Since there is no scale of accelerationunits on the graph, you only need to make the relative magnitudes at the differentlocations consistent with each other.)

0

50

100

0 50 100 150 200 250

Distance (m)

Heig

ht

(m

)

25. Why is it harder to open a door when you push near the hinge than when you pushon the opposite side, away from the hinge?

When you push away from the hinge, you have a longer lever arm.

Since the torque you are applying to the door about the hinge is

the force of your push multiplied by the length of the lever arm,

the torque is higher away from the hinge than close to it.

The acceleration is due to the force of gravity, which

acts only downward.

A page 11 of 12

Calculation4 questions, 4 points each.

The following questions require numerical answers. Show your work, and include theunits with your answers.

26. A single force of 40 N acts upon a 5-kg block. What is the magnitude of theacceleration of the block? (Don’t forget the units!)

27. A rifle fires a bullet with a mass of 5.0 g (0.005 kg). The bullet moves with amuzzle velocity of 1000 m/s after the rifle is fired. What is the momentum of the bulletafter the rifle is fired? (Don’t forget the units!)

F = ma, so a = F/m = (40 N)/(5 kg) = 8 (kg m/s2)/kg = 8 m/s2

p = mv = (0.005 kg)(1000 m/s) = 5 kg m/s

A page 12 of 12

28. A 100-kg mawg (half-man, half-dog) weighs 3000 N on the planet Druidia. Whatis the gravitational acceleration on Druidia? (Don’t forget the units!)

29. A force of 50 N is applied to theend of a wrench handle that is 24 cmlong. The force is applied in a directionperpendicular to the handle as in thediagram. What is the torque (bothdirection and magnitude, includingunits) applied to the nut by the wrench?

F = ma, so a = F/m = (3000 N)/(100 kg) = 30 N/kg = 30 m/s2

This is a crushingly high gravity, about triple that of Earth.

= F r = (50 N)(0.24 m) = 12 Nm

By the right-hand rule, the torque vector is directed into the

plane of the paper, away from you.