Midterm Exam 2 - Siena Science

1 Physics 130 General PhysicsFall 2012 Midterm Exam 2 October 30, 2012 Name:Instructions1. This examination is closed book and closed notes. All your belongingsexcept a pen or pencil and a calculator should be put away and yourbookbag should be placed on the You will find one page of useful formulae on the last page of the Please show all your work in the space provided on each page. If youneed more space, feel free to use the back side of each dishonesty ( , copying or cheating in any way) willresult in a zero for the exam, and may cause you to fail order to receive maximum credit,each solution should have:1. A labeled picture or diagram, if A list of given A list of the unknown quantities ( , what you are being asked to find).

2 4. A force-interaction diagram, if One or more free-body diagrams, as appropriate, with labeled 1D or 2 Dcoordinate Algebraic expression for the net force along each dimension, as An algebraic solution of the unknown variables in terms of theknown A final numerical solution, including units, with a box around An answer to additional questions posed in the problem, if 130 General PhysicsFall 20121. A heavy box is in the back of a truck. The truck is accelerating to the right. Draw amotion diagram, a force-interaction diagram, and a free-body diagram for the :You can see from the motion diagram that the box accelerates to the right along withthe truck. According to Newton s second law,~F m~a, there must be a force to theright acting on the box.

3 This is friction, but not kinetic friction, because the boxis not sliding against the truck. Instead, it is static friction, the force that preventsslipping. Were it not for static friction, the box would slipoff the back of the friction acts in the direction needed to prevent slipping. In this case, frictionmust act in the forward (toward the right) 130 General PhysicsFall 20122. A bag of groceries is on the seat of your car as you stop at a stop light. The bag doesnot slide. Draw a motion diagram, a force-interaction diagram, and a free-body diagramfor the :You can see from the motion diagram that the bag accelerates to the left along withthe car as the car slows down. According to Newton s second law,~F m~a, theremust be a force to the left acting on the bag.

4 This force must bestatic friction, theforce that prevents slipping, because the bag is not slidingacross the seat. Were itnot for static friction, the bag would slide off the seat as thecar stops. Static frictionacts in the direction needed to prevent slipping, and in thiscase, friction must actin the backward (toward the left) 130 General PhysicsFall 20123. A football coach sits on a sled while two of his players build their strength by draggingthe sled across the field with ropes. Assume that the two players pull with equal friction force on the sled is 1000 N and the angle between the two ropes is 20 . Howhard must each player pull to drag the coach at a steady m{s?Solution:The pictorial representation and free-body diagram are shown below:This is a 1D dynamics problem.}

5 The relevant forces are the force of kinetic frictionon the sled and the tension of each rope. Although there is alsogravity, we are giventhe friction force, and therefore we do not need to know the weight of the the sled is not accelerating, it is in dynamic equilibrium along both axes, andNewton s first law applies:pFnetqy Fy T1y`T2y`fky 0 N(1)pFnetqx Fx T1x`T2x`fkx 0 N(2)Examining the free-body diagram, along they-axis we haveT1y `T1sinp {2q(3)T2y T2sinp {2q(4)fky 0.(5)Substituting into equation (1), we getT1sinp {2q T2sinp {2q 0(6) T1 T2 T.(7)4 Physics 130 General PhysicsFall 2012In other words, the tension force of each rope is the the free-body diagram along thex-axis we haveT1x T1cosp {2q Tcosp {2q(8)T2x T2cosp {2q Tcosp {2q.}}}}}}}}

6 (9)Substituting into equation (2) and solving forTwe getTcosp {2q `Tcosp {2q fkx 0(10)2 Tcosp {2q fkx(11) T fkx2 cosp {2q(12)T 1000 N2 cosp20 {2q(13) 508 N 510 N.(14)Note that in the last line we simplified our result to have just two significant 130 General PhysicsFall 20124. You re driving along at 25 m{s with your aunt s valuable antiques in the back of yourpickup truck when suddenly you see a giant hole in the road 55 mahead of you. For-tunately, your foot is right beside the brake and your reaction time is zero! Will theantiques be as fortunate? Assume that the coefficient of kinetic friction for rubber ( ,a tire) on concrete is (a) Can you stop the truck before it falls in the hole?}}}}}}

7 (b) If your answer to part (a) is yes, can you stop without the antiques sliding andbeing damaged? Their coefficients of friction are s and k :To solve this problem we will treat the antiques (mass m) in the back of the pickup(mass M) both as particles. The antiques touch the truck s steel bed, so only thesteel bed can exert contact forces on the antiques. The pickup-antiques system willalso be treated as a particle, and the contact force on this particle will be due to pictorial representation, motion diagram, force-interaction diagram, and free-body diagram for the combined pickup-antiques system are shown below:6 Physics 130 General PhysicsFall 2012 The free-body diagram ofjustthe box of antiques is:(a) Our strategy for solving this problem is to find the smallest coefficient of frictionthat will allow the truck to stop in 55 m, then compare that to the known coefficientsfor rubber on concrete.

8 For the pickup-antiques system, with massm`M, Newton ssecond law ispFnetqx Fx f pm`Mqax pm`Mqa(1)pFnetqy Fy N pFGqP A 0(2) N pm`Mqg 0(3) N pm`Mqg.(4)The model of static friction isf N, where is the coefficient of friction betweenthe tires and the road. Substituting into the equations above, we get f N pm`Mqg pm`Mqa(5) a g.(6)The mass of the pickup-antiques system drops out! Next, from the constant-accelerationkinematics equation withv21 0 andx0 0, we havev21 v20`2apx1`x0q(7) a v202x1(8) min v202gx1(9) p25 m{sq22 m{s2q p55 mq(10) (11)7 Physics 130 General PhysicsFall 2012 Since this is smaller than the coefficient of static friction of rubber on concrete, ,the truckcanstop.}}

9 (b) The analysis of the pickup-antiques system applies to the antiques as well, andgives the same value of min This value is smaller than the given coefficientof static friction ( s ) between the antiques and the truck bed. Therefore, theantiques will not slide as the truck stops over a distance of 55 130 General PhysicsFall 20125. You and your friend Peter are putting new shingles on a roofpitched at 25 . You resitting on the very top of the roof when Peter, who is at the edge of the roof directlybelow you, m away, asks you for the box of nails. Rather than carry the kg boxof nails down to Peter, you decide to give the box a push and have it slide down to the coefficient of kinetic friction between the box and the roof is , with what speedshould you push the box to have it gently come to rest right at the edge of the roof?

10 Solution:The pictorial representation and free-body diagram are shown below:This is a 1D dynamics problem. The relevant forces are gravity,FG, the normalforce,n, and the kinetic friction force,fk. Note that we do not include the initialforce that was applied to the box of nails to get it moving, butwe do include thefact that the box has some initial most natural coordinate system is one that is rotated by 25 and thereforealigned with the roof. The interaction and free-body diagrams are shown net force along thex- andy-axis ispFnetqx Fx FGsin 25 fk ma(1)pFnetqy Fy n FGcos 25 0(2) n FGcos 25 (3)In the second line we used the fact that the shingles are not leaping off the roof toset the acceleration in they-direction equal to zero.