Physics 122 Midterm (Fall 2010)

University of Waterloo Department of Physics & Astronomy Physics 121 midterm examination F totally 2010 Instructors Dr. Robert Mann (sections 2,3) Dr. Guenter Scholz (section 1) Date November 4 , 2009 Time 1900-2100 Duration 2 hours (120 minutes) rh Instructions Important Write your name and student ID on each page. If necessary you whitethorn use the back of the page to confront your answer exactly 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 calculating machine writing implements Question Points Score 1 2 3 4 5 6 Total 20 20 20 20 20 20 1. a Up, up, and a style 15 A balloonist cant resist throwing a revel 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 guide to be thrown to be caught? 1. Logging 10 Estimate, via a commonsense calculation, the number of trees that need to be cut down to supply the anatomy for one days edition of the major newspaper The study in Kitchener-Waterloo2. Circus performance A pivoting pulley hanging from the tenderness tent top allows a lady artist (m = 40 kg) to prove freely while her partner (M = 100 kg) supports her via a lot all 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 draw 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 ladys supporting rope? 6 (d) What is the period ( succession for one revolution) of he r revolution? 3. Going Fishing Because of inclement weather, a boater needs to travel as quickly as workable 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 feed is flowing at 3. 0 km/hr 45 to the southeastward of East, and the boats speed is 8. 00 km/hr relative to the water.B A 5 (a) What is the lintel of the boater for the shortest trip? clearly indicate this angle on an appropriate diagram) 5 (b) Find the boats 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 acquire? m F 4. Blocked Up M A down in the mouth block of mass m proportionalitys on the incline of a thrust of mass M and angle , whose coefficient of static friction is . 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 wee block from sliding down the slope if =0 and 45 o ? 12 (b) For general values of m, M , and , find the minimum force that you need to apply to the wedge that will cause the small block to only if begin to move up the slope. 5. Piano Moving nitwit and energetic are moving a piano of mass M = ccc kg using the pulley system shown in the diagram. The rope roughly the pulley holding the piano, is tied to the axle of the top pulley which in liberate is fastened to the ceiling. ready 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 restless applying to keep the piano hang? 6 (c) Doofus tries to help Diligent by climbing onto the upper broadcast and taking the rope off of the hook attaching the uppermost pulley to the platform, intellection he can help pull from there. How much force mustiness he exert to keep the piano suspended? 3 (d) Doof us finds that he cannot support the weight and lets go of the rope. How long does Diligent have to elude the piano before it hits the ground? 6. Safety First Doofus and Diligent are going to a party.They each buckle themselves in with seatbelts Diligent is hold a 25 kg keg of beer on his swosh while Doofus drives. 4 (a) While travelling 60 km/hr, Doofus has to make an emergency stop over a distance of 45 m. How much force will Diligents arms have to exert on the keg during this deceleration period so that it stays on his bat? 4 (b) The trip continues and the motorcar turns a corner onto a highway, going at 90 km/hr. Suddenly Doofus sees a car heading toward them. He panics, locking the brakes and veering off to the right onto a very steep and muddy road allowance with a station of 35%.The car slides up this nearly frictionless hill and comes to a stop at a cliff edge. How much distance does it big top? 7 (c) From the top of this cliff they can see the location of the party a 2 kilometers east and 1000 meters above where they are. Diligent wants to walk the rest of the way, but Doofus proposes to use the motorized hang-glider in the back of the car to fell over there with the keg. He says he can fly straight there with a speed of 40 km/hr using its 6 horsepower motor, and sets off with the keg.While he is getting ready, Diligent, astute that a horsepower is 750 Watts, calculates how much mass the glider can carry. He looks at the package and sees that air buoyancy alone can evermore support the glider as long as it is not carrying anything but Doofus weighs 75 kg. Can Doofus carry the keg this way? 5 (d) As Doofus takes off, Diligent shouts out how slow he must fly to get to the party. What does he shout?. Useful Formulae Kinematics (a=const) Work, WKE, Power 1 r2 = r1 + v1 (t2 t1 ) + a (t2 t1 ) 2 2 v2 = v1 + a (t 2 t1 ) W = F = Fx x + Fy y + Fz z (constant force) 2 v2 v12 = 2a (r2 r1 ) Circular Motion K= 1 2 mv 2 Kinetic energy W net = K f K i = K ar = ac = v2 r at = dv dt (uniform motion) P= P= W t dr dW =F = F v dt dt T U = 2 r dist = speed v Newtons Laws F net = F = ma F12 = F21 Fg = mg Math ? A + B = ( Ax + Bx )i + ( Ay + B y ) ? j A B = Ax Bx + Ay B y Fs (x) = kx sin 2 + cos 2 = 1 f s f s ,max = s n f k = k n congress Motion sin A sin B sin C = = a b c a 2 = b 2 + c 2 2bc cos A v AB = v A vB