Instructors:

Dr. Robert Mann (sections 2,3) Dr. Guenter Scholz (section 1)

Date: November 4 , 2009 Time: 19:00-21:00 Duration: 2 hours (120 minutes)

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Instructions

Important: Write your name and student ID on each page. If necessary you may use the back of the page to continue your answer but not the back of the previous page. The pages may be separated as part of the marking process. 5 questions constitute a complete paper. Each question is of equal value. All questions will be counted. The last page contains some constants and formula that may be useful. You may remove and keep this page as a souvenir.

Aids Permitted

calculator writing implements

Question

Points

Score

1 2 3 4 5 6 Total:

20 20 20 20 20 20

1.a Up, up, and away [15] A balloonist can’t resist throwing a drink to another balloonist. The ‘thrower’ is moving at v = -15j m/min while the ‘catcher’ is moving at v = 15j m/min. At the instance the former throws the drink the ‘catcher’ is at (3i – 10j) m from the ‘thrower’. If the throw is horizontal, at what speed does the drink need to be thrown to be caught?

1.b Logging [10] Estimate, via a reasonable calculation, the number of trees that need to be cut down to supply the pulp for one day’s edition of the major newspaper “The Record” in Kitchener-Waterloo

2. Circus performance A pivoting pulley hanging from the center tent top allows a lady artist (m = 40 kg) to rotate freely while her partner (M = 100 kg) supports her via a rope over the pulley. he rope length, measured from the pulley, holding the rotating artist is 3.0 m and the helper is not accelerating. [4] (a) Draw a Free Body Diagram of each performer and the pulley; clearly indicate the forces.

[5] (b) What is the tension in the rope?

[5] (c) At what angle, with respect to the vertical, is the lady’s supporting rope?

[6] (d) What is the period (time for one revolution) of her revolution?

3. Going Fishing Because of inclement weather, a boater needs to travel as quickly as possible across a channel from a fishing spot at ‘A’ to the harbour at ‘B’. The harbour is 10.0 km East and 15 km North of his fishing spot. A tide is flowing at 3.0 km/hr 45 to the South of East, and the boat’s speed is 8.00 km/hr relative to the water.

B

A

[5] (a) What is the heading of the boater for the shortest trip? (clearly indicate this angle on an appropriate diagram)

[5] (b) Find the boat’s speed relative to the shore.

[5] (c) What is the shortest time for the trip?

[5] (d) If there were no tide, how much time would the trip require?

m

F

4. Blocked Up

M

!

A small block of mass m rests on the incline of a wedge of mass M and angle ! , whose coefficient of static friction is µ. The wedge is on a frictionless surface.

[8]

(a) If m = 1 kg and M = 20 kg, what is the minimum force, F, you need to apply to the wedge that will prevent the small block from sliding down the slope if µ =0 and ! =45 o ?

[12]

(b) For general values of m, M ,! and µ, find the minimum force that you need to apply to the wedge that will cause the small block to just begin to move up the slope.

5. Piano Moving

Doofus and Diligent are moving a piano of mass M = 300 kg using the pulley system shown in the diagram. The rope around the pulley holding the piano, is tied to the axle of the top pulley which in turn is fastened to the ceiling. Diligent is holding the rope at the left, suspending the piano 10 metres above the ground. [4]

(a) Draw free-body diagrams of the piano and of each pulley. Be sure to include all relevant forces.

[7] (b) How much force is Diligent applying to keep the piano suspended?

[6] (c) Doofus tries to help Diligent by climbing onto the upper platform and taking the rope

off of the hook attaching the uppermost pulley to the platform, thinking he can help pull from there. How much force...