Physics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10

Transcription

1 There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference frae is one in which (a) Newton s first law describes the behaviour of atter. (b) the law of inertia is not applicable. (c) there is a great deal of atter. (d) the object of interest is traveling in a circular path. (e) forces do not necessarily exist in pairs. 2. A lap with a ass is suspended fro the ceiling by two cords as shown. The ratio of the agnitude of the vertical coponent of the tension in T 2 to that in T 3 is 4. A car experiences both a centripetal and a tangential acceleration. For which of the following would this be true? (a) It is going around a curve at a constant speed. (b) It is going around a curve and slowing down. (c) It is going along a straight road at a constant speed. (d) It is going along a straight road and increasing its speed. 5. If echanical work is done on a body, the body ust (a) accelerate. (b) be in equilibriu. (c) not exert any force. (d) have no friction force exerted on it. (e) ove (a) 1:1 (b) 1:2 (c) 3:1 (d) 3:2 (e) 3:1 The ratio of the agnitude of the tensions T 1 : T 2 is (3) : 1 but the question is asking for the ratio of the vertical coponents so the answer is 3:1. Read carefully! 3. Two objects are sliding at the sae speed across a wooden surface. The coefficient of kinetic friction between the first object and the surface is twice that between the second object and the surface. The distance traveled by the first object before it stops is S. The distance traveled by the second object is (a) ipossible to deterine without knowing the asses involved. (b) 2S (c) S/2 (d) S (e) 4S 6. Power P is required to lift a body a distance d at a constant speed v. What power is required to lift the body a distance 2d at constant speed 3v? (a) P (b) 2P (c) 3P (d) 6P (e) 3P/2 7. The potential energy function for a conservative force acting in the x direction is shown in the figure on the right. Where would the particle experience a force directed to the right? (a) fro A to B and fro E to F (b) at points B and D (c) fro B to C and fro C to D (d) at points C and E (e) fro B to C and fro D to E 1

2 8. The work done by a conservative force between two points is (a) always positive. (b) zero. (c) always dependent upon the tie. (d) never copletely recoverable. (e) always independent of the path. 9. The condition necessary for the Conservation of Linear Moentu in a given syste is that (a) energy is conserved. (b) internal forces equal external forces. (c) one body is at rest. (d) None of these is correct. (e) the net external force is zero. 10. A oving particle is stopped by a single head-on collision with a second, stationary particle if the oving particle undergoes (a) an elastic collision with a second particle of uch saller ass. (b) an inelastic collision with a second particle of any ass. (c) an elastic collision with a second particle of uch greater ass. (d) an elastic collision with a second particle of equal ass. (e) any type of collision in which the coefficient of restitution is zero. 2

3 There are four written probles. Show all your work and explain your reasoning to get full credit. 11. Two blocks are on two adjacent inclined raps and they are connected through a rope over a assless, frictionless pulley as shown in the figure. The left-hand block has ass M = 2.0 kg and the right-hand one = 1.2 kg. The angles of incline at the base of the raps are θ and φ. [10] (a) Draw the free body diagras for both blocks assuing there is no friction. F N1 Mg F T F T g F N2 θ The vectors should be labelled. The tension is assued the sae because the pulley is assless: F T. However, it s iportant that the noral forces be labelled differently: F N1 and F N2 because the asses are different. Also the weights are Mg and g respectively. If you failed to distinguish the different noral forces or weights you ay not have got full arks. (b) If θ = 30 and the blocks are in equilibriu and don t slide either way, find the angle φ ( ) M sin θ φ = arcsin Ver a: φ = 56.4 Ver b: φ = 47.3 (c) Block suddenly develops soe friction: µ s = 0.6 and µ k = 0.4. how uch saller can you ake θ and still not have the blocks slide? (Block M is still frictionless.) F N2 F T M φ g F f Another free body diagra for ass called for here. If you can do it without the FBD then good on ya, but you re uch ore likely to ake a istake without it. Answers showing the new FBD will be graded leniently even if the answer is nuerically wrong. Ver a: θ = Ver b: θ = 10.2 ( ) (sin φ θ µs cos φ) = arcsin M (d) When the angle is adjusted so that it just starts sliding. What is the agnitude of acceleration of the asses? a = g ( (sin φ µ k cos φ) sin θ M) M + Ver a: a = 0.41 /s 2 Ver b: a = 0.54 /s 2 3

4 12. In a variation of the circular otion experient you did, the ass below the tube M and the rotating ball of ass are always the sae. The length of the string fro the top of the tube to the centre of ass of the ball L is varied and the period of rotation which establishes equilibriu is deterined at each length. A straight-line plot is obtained, the slope of which can be used to deterine the value of the ball s ass. [10] (a) The weight M = 200 gras and L = 0.5. You tie the rotational period to be T = 0.7 s. Fro these data calculate the ass of the whirling thing? L ver a: = kg ver b: = kg = g M T 2 4 π 2 R (b) You vary the L several ties and easure T each tie. The relationship is L = KT n. Find sybolically K and n assuing that the theory of unifor circular otion applies. K = g M 4 π 2 n = 2 (c) If you plot L vs T n you get a straight line whose slope can be used to calculate the ass. Given a slope of 1.0 s 2 /, what is the ass of the object? ver a: = kg ver b: = kg = g M 4 π 2 K M 4

5 13. A bullet with ass 20 gras and velocity 100 /s collides with a wooden block of ass 2 kg. The wooden block is initially at rest, and is connected to a spring with k = 800 N/. The other end of the spring is attached to an iovable wall. What is the axiu copression of the spring? Note: You ay assue that the spring is assless and that the collision between the bullet and the wooden block is copletely inelastic.[10] (a) Write down the equation for the initial oentu p i in ters of the following quantities (You do not have to use all of the): The ass of the rubber bullet,. The ass of the block, M. The spring constant, k. The initial velocity of the bullet, v i. The final velocity of the block together, v f. The final oentu, p f. p i = v i (b) Write the equation for p f using the variables entioned in the previous section. ust be coplete, not just p f = p i. p f = p i = ( + M)v f (c) Write the equation for the final velocity v f of the block v f = + M v i (d) What is the expression for axiu copression of the spring? x ax = 2 v 2 i k( + M) = v i k( + M) Extra credit if they checked the units of the final expression. Nuerical evaluation is optional. 5

6 14. A 60 gra tennis ball elastically hits a 500 gra stationary cart whose wheels have no friction. The tennis ball is oving at 5 /s. [10] (a) What is the velocity of the centre of ass? ver a: /s, ver b: /s v c = v i + M (b) What are the velocities of the ball and the cart in the centre-of-ass frae of reference before the collision? ver a: /s, /s ; ver b: 4.03 /s, /s v 1,i = v 1,i v c v 2,i = v 2,i v c (c) What are the velocities after the collision in the c.. reference frae? ver a: /s, 0.536/s ; ver b: 4.03 /s, /s v 1, f = v 1,i v 2, f = v 2,i (d) What are the velocities of the ball and cart after the collision in the earth s reference frae? ver a: /s, 1.07 /s; ver b: /s, /s v 1, f = v 1, f + v c v 2, f = v 2, f + v c 6