Phyic 160-0 Sp. 017 Exa #3 Nae: 1) In electrodynaic, a agnetic field produce a force on a oving charged particle that i alway perpendicular to the direction the particle i oving. How doe thi force affect the kinetic energy of the particle? Explain. Since the force i ALWAYS perpendicular to the direction of otion, it cannot do any work ince W = Fdco. Since no work, no tranfer of energy, and hence no change in kinetic energy. I doe, however, affect the direction of otion - an electron will ove in a circle in a agnetic field. ) A arble ove along the x-axi. The potential-energy function i hown below. Decribe the force (agnitude and direction) on the arble at the four labeled point. U The force i related to the potential by Fx. The x derivative of the potential function i zero at point b and d, o that where the force i alo zero. At point a, the derivative i E negative, o the force i poitive (and ha a relatively large agnitude). At point c, the derivative i poitive, o the force i negative (pointing in the negative x-direction) and i a bit le trong than at point a. 3) If the arble above ha a total energy E a arked, decribe the peed of the arble at the four labeled point. The kinetic energy of the arble i given by the total energy inu the potential energy, o, at point b, the kinetic energy (and hence, the peed) i the highet and at point d it i zero. At point a and c, the peed i the ae.
4) Block A in the figure below ha a.00 kg, and block B ha a 5.00 kg. The block are forced together, copreing a pring S between the; then the yte i releaed fro ret on a level, frictionle urface. The pring, which ha negligible a, i not fatened to either block and drop to the urface after it ha expanded. Block B acquire a peed of 1.0 /. How uch potential energy wa tored in the copreed pring?.00 kg 5.00 kg Since there are no net outide force, the total oentu of the yte ut reain contant:, but ince nothing i oving before the block are p releaed: 0 p v v f A A B B i p f 0.00kg va 5.00kg 1. kg va 6.00.00kg 3.00 Then, we alo know fro energy conervation that the pring potential energy wa converted to kinetic energy of the two block: 1 1 Uel KETot AvA BvB 1 1.00kg 3.00 5.00kg 1.0 9.00J 3.60J 1.60J
5) Find the location of the center of a of the object below. (Take the hinge to be ale, and place the origin at the hinge.) Taking the location of the hinge to be the origin, x y CM CM 4.00kg 0.75 3.00kg 0.00kg 0 9.00kg 0.33 4.00kg 0 3.00kg 0.90.00kg 1.80 9.00kg 0.70 6) A rocket i fired traight upward on a windle day. At the peak of it trajectory, it explode into two part, one with three tie the a a the other. Both piece trike the ground at the ae tie. You find the heavy piece 10 to the Eat of the launch ite. Where hould you look for the lighter piece? Aue no air reitance. Since the center of a wouldn t ove (no outide force in the horizontal direction) the center of a would reain at the launch ite. The center of a i cloer to the heavier object, o the lighter object i farther fro the launch ite. If we put x=0 at the launch ite, then we have xcm 0 103M xlight 1M, x 30 light or 30 Wet of the launch ite.
7) A yte of two paint bucket connected by a lightweight rope (over a ale pulley) i releaed fro ret with the 1.0 kg bucket.00 above the floor. During the tie that the 1.0 kg bucket drop to the floor, friction in the pulley reove 10.0 J of energy fro the yte. What i the peed of the bucket when it hit the floor? Fro conervation of energy, the net change in echanical energy i the work done by friction, o E W K U U ech fk g el f 0 f 0 f 0 f 0 4kg 1kg 4kg 1kg 4kg 1kg 4kg 1kg 10J 1 v 1 v 1 v 1 v gy gy gy gy 10J 1 v 1 v gy 0 0 gy 10J 1 1kg 4kg v 4kg g 1kg g v 10J 8kg 4kg 9.8 8kg 8kg 9.8 8kg v 18.4 v 4.8
A bullet of a 5.0 g i fired horizontally into a.0 kg wooden block at ret on a horizontal urface. The coefficient of kinetic friction between block and urface i 0.5. The bullet top in the block, which lide traight ahead for.5 (without rotation). 8) What i the peed of the block iediately after the bullet top in it? Friction doe work on the block to top it. The agnitude of the frictional force i (eq. 3) Ff = 0.5*(.005kg*9.8/ )=4.91N and act on the block for.5, o fro eq., W=Fd=-4.91N*.5=-1.3J. Thi will repreent a change in the kinetic energy (eq. 7 & 8). So v = qrt(*1.3n/.005kg) = 3.50/. 9) At what peed i the bullet fired? Moentu i conerved in the colliion, o vbefore = vafter or 0.005kg*v=(.0kg+0.005kg)*3.50/ o v = 1400/.
10) A all hockey puck of a 1 kg lide without friction over the icy hill hown below. At the top of the hill, it encounter a rough horizontal urface (coefficient of kinetic friction = 0.4) and hit a pring with pring contant k = 400N/, copreing it by 0. before it top. The total ditance it travel over the rough urface i.0. What wa the initial peed of the puck?.0 5.0 10.0 Fro conervation of energy, the net change in echanical energy i the work done by friction, o E W K U U 0 ech f g el k k 1 1 0 0 1 1 0 0 1 0 0 1 0 F d v v gy gy kx kx f f f f F d v gh kx k N f gd 1 v gh 1 kx k 0 f N 400 k v0 kgd gh x f 0.4 9.8 9.8 5 0. 1kg v v 0 15.7 98 16 11.4