Chapter 8

Question 1

A woman runs up a flight of stairs. The gain in her gravitational potential energy is U. If she runs up the same stairs twice the speed, what is her gain potential energy?

Answer 1

U

Question 2

Susana ascends a mountain via a short, steep trail. Sean ascends the same mountain via a long, gentle trail. Which of the following statements is true?

Answer 2

Susana gains the same gravitational potential energy as Sean.

Question 3

The reference point for gravitational potential energy

Answer 3

Can be chosen arbitrarily

Question 4

Which of the following statement about potential and kinetic energy is true?

Answer 4

Potential energy can be negative but kinetic energy cannot.

Question 5

Calculate the work down by a force, F=2x i + 4y j, around a closed path, first going from P1 (1,1) to P2 (4,4) along path a and returning along path b.

Answer 5

0J because they are the same

Question 6

When potential energy U(r) is given as in Figure A, then the force in Figure B is given by which curve?

Answer 6

Straight line (negative if Figure A is negative)

Question 7

Which of the following statements about conservation is true?

Answer 7

A conservative force cannot change a body’s total energy.

Question 8

Which potential energy versus displacement curve best represents that of an extended spring?

Answer 8

Upside down half parabola coming from zero

Question 9

The potential energy function for a conservative force acting in the x direction on a particle is shown below. The points where the net force on the particle is equal to zero are

Answer 9

2, 3, 4, and 5

the dips and hills in the middle (not the end points)

Question 10

A skier of mass 50 kg is moving at speed 10 m/s at point P1 down a ski slope with negligible friction. What is the skier’s kinetic energy when she is at point P2, 20m below P1?

Answer 10

12300 J

LOOK UP

Question 11

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

Answer 11

mv^2/r

Question 12

The total mechanical energy of any system is

Answer 12

The sum of the kinetic and potential energy at any point

Question 13

A body falls through the atmospher gaining 20 J of kinetic energy. Air resistance is NOT negligible. How much gravitational potential energy did it lose?

Answer 13

More than 20 J

Question 14

A projectile of mass m is propelled from ground level with an initial kinetic energy of 450 J. At the exact top of its trajectory, its kinetic energy is 250 J. To what height, in meters, above the starting point does the projectile rise? Assume air resistance is negligible.

Answer 14

200/(mg)

Question 15

A block of mass m is pushed up against a spring, compressing it a distance x, and is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed of 3v. What is the distance the spring compressed in the second case?

Answer 15

6x

Question 16

Release mass m on a string from rest at point A. As it passes the lowest point B, the tension in the string is

Answer 16

2 mg
T = (3-2cose theta)mg
Cos theta = 1/2 T = 2mg

Question 17

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?

Answer 17

The center of mass is to the left of the center of gravity

Question 18

A mass m1, attached to a spring is placed on a cart with mass m2, which moves freely and without friction on a table. The mass m1 slides without friction on the cart and is 1/4 the mass of m2. When m1 is allowed to oscillate along m2, what is the motion of m2?

Answer 18

m2 moves in the opposite direction of m1