Page 1 of 7

PHY117 Practice Exam 3 (Mostly from Fall 2014)

Problem 1 (15 pts) Some Conceptual Questions a) Two balls (A and B) are spinning around in horizontal circles on a frictionless table. They are connected by strings to pegs that stick out of the table. For each case below (describing each balls mass, the radius of its circular motion, its speed, and/or its angular velocity) say whether the tension is greater in string A, greater in string B, or equal for the two.

i. ! = !, ! = !, ! = 2!

ii. ! = !, ! = 2!, ! = !

iii. ! = 2!, ! = !, ! = !

iv. ! = !, ! = 2!, ! = !

v. ! = !, ! = 2!, ! = !/2

Page 2 of 7

b) Below is a graph of the monkey and the banana problem. The banana (empty diamonds) is launched horizontally towards the monkey (empty square). Solid circles represent the center of mass. The monkey does not catch the banana. Instead the banana bounces right off the monkey. Sketch the motion of the center of mass after the collision.

-0.2 0.0 0.2 0.4 0.6 0.8 1.00.00.5

1.0

1.5

2.0

x(m)

y(m)

Page 3 of 7

Problem 2 (30 pts) A Really Bad Idea A 65 kg skier decides to get his 25 kg suitcase down a mountain by towing it behind him. You may assume that there is negligible friction between the man and the mountain, while the coefficient of kinetic friction between the suitcase and the mountain is 0.20. The mountain is at a 25 angle, as shown below. Find the acceleration of the man and suitcase. (There are a number of reasons why this is a bad idea; to see one of them, consider what happens when the man stops!) The first three steps of the problem solving framework are required for this problem: key

ideas, picture and calculations. You do not need to write an assessment.

25

Page 4 of 7

Problem 3 (25 pts) On a Tilt The picture below* shows a fair ride in which riders lean back against a slanted wall in a room that starts spinning. Assume a 55 kg woman is on the ride and the tilt of the wall is 72 degrees (where 90 degrees would be a normal, vertical wall). The wall is 4.8 meters from the center.

a) Find the minimum angular velocity that the ride must have so the woman will not slide down the wall assuming her clothing has no friction with the wall.

b) Still assuming negligible friction, what will happen to the woman if the ride spins faster than the speed you just found?

The first three steps of the problem solving framework are required for this problem: key ideas, picture and calculations. You do not need to write an assessment.

* http://www.ride-extravaganza.com/intermediate/gravitron/

Page 5 of 7

Problem 4 (30 pts) Center of Mass of a Trapezoid A flat piece of wood of uniform density is cut into the shape of the trapezoid shown below. (Dont worry if you didnt know what a trapezoid is; its the shaded shape shown below.) The trapezoid has height H, the lower edge has length L, and the upper edge extends a distance D past the lower edge.

a) Find the y (vertical) position of the center of mass of the trapezoid. Your answer should be a formula, not a number.

b) Now let = 3.0, = 2.5, = 1.0. Find a numerical value for !"#. All four steps of the expert problem solving framework are required for this problem, but your assessment should only be for part b.

D

H

x

y

L

Page 6 of 7

Extra Credit (5 pts) A rod extends from = 0 to = . At each point the metal on the rod reflects a fraction = (/)! of the light that hits it. If light is shining uniformly on the surface, what fraction of the total light hitting the surface is reflected? This problem is extra credit. I do not recommend working on it until you are confident you have finished all of the regular problems.

Page 7 of 7

Some possibly useful mathematical symbols and formulas Exam 3 Constant acceleration For the specific case where an object has a constant acceleration (a) in any direction the motion in that direction is described by

0

2

0 0

2 2

0 0

1

2

2 ( )

x x x

x x

f

v v a t

x x v t a t

a x x v v

= +

= + +

=

(Be careful in using these formulas to make sure you use correct signs.) Friction Static friction: Nsfr FF Kinetic friction: Nkfr FF = Rotation Converting between translation and rotation: RvRs TT == ,

Rva lcentripeta /2=

Center of Mass xCOM =

m1x1 +m2x2 + ...M , yCOM =

m1y1 +m2y2 + ...M , zCOM =

m1z1 +m2z2 + ...M

For a continuous object the sum in the numerator has to be evaluated as an integral. xCOM =

1M xdm , yCOM =

1M ydm , zCOM =

1M zdm

Some general formulas and definitions Uncertainty of the average of N data points with random error: . /SDOM Std Dev N= Uncertainties in a sum or difference: nxxxq +++= ...21 Uncertainties in a product or quotient: 1 1 2 2/ / / ... /n nq q x x x x x x = + + +

Uncertainty for a function of one variable q = dq

dx xbest x

The quadratic formula: If 02 =++ cbxax , then [ ]acbba

x 421 2 = .

Gravitational acceleration near Earths surface: g = 9.8 m/s2 Unit conversions: 1 km = 1000 m. 1 m = 100 cm = 1000 mm = 3.28 ft. 1 inch = 2.54 cm. 1 mile=5,280 ft. 1 m/s= 2.24 mi/hr. 1 N = 0.225 lb. A 1 kg object weighs 2.2 lbs. (sin( )) / cos( ), (cos( )) / sin( ), ( ) /x xd x dx x d x dx x d e dx e= = = .