Quiz 2-2

 

If you must leave the room for any reason to include, but not limited to         a.  getting water       b.  checking the room number   do so now, not after the quiz has been distributed

 

 

 

Part 1: Conceptual Questions

Circle the Correct Answer

 

1.  A brick is moving at a speed of 3 m/s and a pebble is moving at a speed of 5 m/s.  If both

     objects have the same kinetic energy, what is the ratio of the brick's mass to the rock's

     mass?

 

     A) 25 to 9   Answer: A

 

     B) 5 to 3

 

     C) 12.5 to 4.5

 

     D) 3 to 5

(1/2)9m_b = (1/2)25m_p

m_b/m_p = 25/9

 

2.  A 4.0-kg mass is moving with speed 2.0 m/s.  A 1.0-kg mass is moving with speed 4.0 m/s.

     Both objects encounter the same constant braking force, and are brought to rest.  Which

     object travels the greater distance before stopping?

 

     A) the 4.0-kg mass

 

     B) the 1.0-kg mass

 

     C) Both travel the same distance.    Answer: C

 

     D) cannot be determined from the information given

 

work = change in kinetic energy = same for both

work = Fd     force is same so distance must be same

 

 

3.  A planet of constant mass orbits the Sun in an elliptical orbit.  Neglecting any friction effects,

     what happens to the planet's kinetic energy?

 

     A) It remains constant.

 

     B) It increases continually.

 

     C) It decreases continually.

 

     D) It increases as planet approaches the Sun, decreases as it moves away.    Answer: D

 

Total mechanical energy = kinetic energy plus potential energy = 1/2mv² + mgy

The total is constant (y is distance from the planet)

If y decreases (as it nears the Sun) then the potential energy must increase and vice versa

 

 

4.  The quantity 1/2 kx2 is

 

     A) the kinetic energy of the object.

 

     B) the elastic potential energy of the object.     Answer: B

 

     C) the work done on the object by the force.

 

     D) the power supplied to the object by the force.

 

As derived and discussed in the text

 

 

5.  Is it possible for a system to have negative potential energy?

 

     A) Yes, as long as the total energy is positive.

 

     B) Yes, since the choice of the zero of potential energy is arbitrary.      Answer: B

 

     C) No, because the kinetic energy of a system must equal its potential energy.

 

     D) No, because this would have no physical meaning.

 

Only true statement

 

6.  A 0.200-kg mass attached to the end of a spring causes it to stretch 5.0 cm. If another

     0.200-kg mass is added to the spring, the potential energy of the spring will be

 

     A) the same.

 

     B) twice as much.

 

     C) 3 times as much.

 

     D) 4 times as much.   Answer: D

 

W = Fx = max = potential energy = (1/2)kx² 

if m is doubled, 2max = ma(2x)

The x for PE is doubled which results in the PE being 4 times as much because of the square

 

 

7.  The total mechanical energy of a system

 

     A) is equally divided between kinetic energy and potential energy.

 

     B) is either all kinetic energy or all potential energy, at any one instant.

 

     C) can never be negative.

 

     D) is constant, only if conservative forces act.     Answer: D

 

The only true statement

 

 

8.  Describe the energy of a car driving up a hill.

 

     A) entirely kinetic

 

     B) entirely potential

 

     C) both kinetic and potential      Answer: C

 

     D) gravitational

 

Kinetic since it is moving and potential (in relation to some reference point)

 

 

9.  Consider two masses m1 and m2 at the top of two frictionless inclined planes.  Both masses

     start from rest at the same height.  However, the plane on which m1 sits is at an angle of 30°

     with the horizontal, while the plane on which m2 sits is at 60°.  If the masses are released,

     which is going faster at the bottom of its plane?

 

     A) m1 

 

     B) m2 

 

     C) They both are going the same speed.      Answer: C

 

     D) cannot be determined without knowing the masses

 

Since they start at the same height, the PE of the two are equal. The KE for each is 0.  The mechanical energy of both (equal) is converted to the same kinetic energy at the bottom, so the velocities are equal (same as the class demo)

 

10.  A ball falls from the top of a building, through the air (air friction is present), to the ground

       below.  How does the kinetic energy (K) just before striking the ground compare to the

       potential energy (U) at the top of the building?

 

      A) K is equal to U.

 

      B) K is greater than U.

 

      C) K is less than U.      Answer: C

 

      D) It is impossible to tell.

 

 

 It is less because some of the energy was converted to heat through friction

Part 2: Quantitative Questions

Circle the Correct Answer

 

1.  An object is lifted vertically 2.0 m and held there.  If the object weighs 90 N, how much work

     was done in lifting it?

 

     A) 360 J

 

     B) 180 J     Answer: B

 

     C) 90 J

 

     D) 0 J

 

W = Fd = 90x2 = 180 J

 

 

2.  You lift a 10-N physics book up in the air a distance of 1.0 m, at a constant velocity of 0.50

     m/s.  What is the work done by the weight of the book?

 

     A) +10 J

 

     B) -10 J      Answer: B

 

     C) +5.0 J

 

     D) -5.0 J

 

W = Fd = (10)(1.0) = -10 J

Negative because the force (weight) of the book is opposite the direction of motion

 

 

3.  A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m. 

     What is the work done by the 5500 N force?

 

     A) 2.75 × 10⁵ J      Answer: A

 

     B) -2.45 × 10⁵ J

 

     C) 3.00 × 10⁴ J

 

     D) -5.20 × 10⁵ J

 

W = Fd = (5500)(50 = 2.75x10⁵

Same direction in this case

 

 

4.  A  30-N box is pulled  6.0 m up along a 37° inclined plane.  What is the work done by the

     weight (gravitational force) of the box?

 

     A) - 11 J

 

     B) - 1.1  × 10²J     Answer: B

 

     C) - 1.4 × 10² J

 

     D) - 1.8 × 10² J

 

W = Fd = (30)(sin37)(6.0) = (30)(0.6)(6.0) = -1.1x10² J

Negative because the weight acts in direction opposite the motion

 

 

5.  A 10-kg mass is moving with a speed of 5.0 m/s.  How much work is required to stop the

     mass?

 

     A) 50 J

 

     B) 75 J

 

     C) 100 J

 

     D) 125 J     Answer: D

 

 Work = change in KE = (1/2)(10)(5)² = 125 J

 

6.  A spring-driven dart gun propels a 10-g dart.  It is cocked by exerting a force of 20 N over a

     distance of 5.0 cm.  With what speed will the dart leave the gun, assuming the spring has

     negligible mass?

 

     A) 10 m/s

 

     B) 14 m/s     Answer: B

 

     C) 17 m/s

 

     D) 20 m/s

 

PE converted to KE

W = Fx = (20N)(0.05m) = 1 J = (1/2)(0.01 kg)v² gives v = (2/0.01)^1/2 = 14 m/s

 

 

7.  A 100-N force has a horizontal component of 80 N and a vertical component of 60 N.  The

      force is applied to a box which rests on a level frictionless floor.  The cart starts from rest,

      and moves 2.0 m horizontally along the floor.  What is the cart's final kinetic energy?

 

     A) 200 J

 

     B) 160 J     Answer: B

 

     C) 120 J

 

     D) zero

 

W = energy = Fd = (80)(2.0) = 160 J

 

8.  An arrow of mass 20 g is shot horizontally into a bale of hay, striking the hay with a velocity

     of 60 m/s.  It penetrates a depth of 20 cm before stopping.  What is the average stopping

     force acting on the arrow?

 

     A) 45 N

 

     B) 90 N

 

     C) 180 N     Answer: C

 

     D) 360 N

SUBMIT DETAILED SOLUTION BY START OF NEXT CLASS FOR INCREASE IN GRADE

Using the work energy theorem, W = change in kinetic energy

1/2mv₂² - 1/2mv₁² =  0 - 1/2(0.020 kg)(60m/s)²

W = -36 J

W = Fd results in -36 = Fd = F(0.2m)

F = 180 N

 

 

9.  A 10-kg mass, hung onto a spring, causes the spring to stretch 2.0 cm. What is the spring

     constant?

 

     A) 4.9 × 10³ N/m     Answer: A

 

     B) 5.0 × 10³ N/m

 

     C) 20 N/m

 

     D) 2.0 N/m

 

SUBMIT DETAILED SOLUTION BY START OF NEXT CLASS FOR INCREASE IN GRADE

F_average = (0 + (10)(9.8))/2 = 49 N

F_averagex = 1/2kx²

(49)(0.02) = (1/2)k(0.02)²

k = 4900 N/m

 

10.  A toy rocket, weighing 10 N, blasts straight up from ground level with a kinetic energy of 40

       J.  At the exact top of its trajectory, its total mechanical energy is 140 J.  To what vertical

       height does it rise?

 

      A) 1.0 m

 

      B) 10 m     Answer: B

 

      C) 14 m

 

      D) 24 m

SUBMIT DETAILED SOLUTION BY START OF NEXT CLASS FOR INCREASE IN GRADE

The total energy is conserved

Take positive as up

The apparent increas in energy (40 - 40 = 100 J) is converted to potential energy at the top which has a negative sign so total energy is conserved

100 = mgh = (10/9.8)9.8h

gives h = 10 m

 

 

Part 3: Review Problems

Show All Work

 

1.  A 4 kg ball is dropped from a height of 8 meters  How long does it take to reach the ground?

 

y = y₀ + v_oyt + 1/2gt²

 

8 = 0 + 0 + 0.5(9.8)t²

 

t = (8/4.9) = 1.6 s

 

2.  A 24 kg box is resting on a 45 degree incline.  What is the normal force?

 

F_N = (24)(9.8)cos45⁰ = (24)(9.8)(0.7) = 165 N

 

3.  A 4 kg object is traversing a circular route with a constant speed of 3 m/s. The route has a

     diameter of 6 meters.  The force holding it in the route is provided by friction.

 

     a.  What is the centripetal acceleration of the object?

 

r = 6/2 = 3 m

 

a_r = v²/r = (3)² /(3) = 3 m/s²

 

     b.  What friction force is required?

 

F = ma_r = m v²/r = (4)(3) = 12 N

 

Part 4: Extra Credit

 

1.  My picture as a child is on the left side of the cover page.  During my early years, some

     thought I had no talent (the dummies!). I worked in a patent office until Max Planck realized

     the importance of some papers I published in 1905. My name is: _____________________

     Albert Einstein

 

2.  Heisenberg (uncertainty principle and quantum mechanics), Newton (Principia, etc.),

     Galileo (Father of Science), and Feynman (Feynman diagrams, etc.) are 4 pioneers in

     physics that I have discussed many times. List them below in order of birth date (one born

     first is listed as A and one born last is listed as D).

 

      You must get the entire sequence correct to receive credit.

 

A.  Galileo

B.  Newton

C. Heisenberg

D. Feynman