review&forexam&2& - physics and astronomy at...

Review for Exam 2 Exam Informa+on 11/24/14 – Monday 7:30 PM All Sec+ons 505-‐509 à MPHY 205 (this room, 30 min a.er class ends) Dura+on à 1 hour 15 min Ø  Know your instructor’s name (S+egler) and your sec+on number (505 -‐ 509) Ø  Have your TAMU ID ready to show when turning in your exam. Ø  Calculators are allowed, no pre-‐saved data on them, if you are caught using previously saved data

it will be considered chea=ng and dealt with accordingly. Exam Structure Ø  4 mul+ple choice ques+on

•  You do not need to show your work on these. •  There is no par+al credit.

Ø  3 long problems •  The problems will be similar to homework problems of medium difficulty. •  There will be a mix of ‘numeric’ and ‘symbolic’ problems. •  Par+al credit is given, you must show your work clearly.

T. S+egler 11/19/2014 Texas A&M University

Problem 3*

A 15.0 kg block is a[ached to a very light horizontal spring (k = 500 N/m) and is res+ng on a fric+onless horizontal table. Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the le]. Find the maximum distance that the block will compress the spring a]er the collision.


Problem 4*

A 5.00 kg ornament is hanging by a 1.50 m wire when it is suddenly hit by a 3.00 kg missile traveling horizontally at 12.0 m/s. The missile embeds itself in the ornament during the collision. What is the tension in the wire immediately a]er the collision?


Problem 5* A woman whose mass is 70.0 kg stands at the rim of a horizontal turntable that has a moment of iner+a 300 kg m2 and radius of 2.00 m. The system is ini+ally at rest and is free to rotate about fric+onless ver+cal axle through the center of the turntable. The woman begins to walk clockwise around the rim at a speed 1.50 m/s rela+ve to the earth. a) In what direc+on and with what angular speed does the turntable rotate? b) How much work does the woman do to set the system (woman plus turntable) in mo+on?


Problem 6* Two blocks are suspended over a pulley with a string of negligible mass as shown below. One block has mass m1 = 1.00 kg, the other one has a mass of m2 = 2.00 kg. The pulley is a uniform solid cylinder. The string does not slip on the pulley and the center of mass of the pulley remains sta+onary. The downward accelera+on a, of mass m2 is measured to be a = g/4. a) What is the mass, M, of the pulley? b) If you replaced the pulley by a hollow cylinder of the same mass and radius, the downward accelera+on of mass m2 would be .

m1 m2

a


Problem 6* -‐ cont. b) If you replaced the pulley by a hollow cylinder of the same mass and radius, the downward accelera+on of mass m2 would be .

m1 m2

a


Problem 8* You have a horizontal table with a fric+onless top and a hole in the center. A string through this hole is suppor+ng a hanging mass m1 = 0.35kg. The end on the top of the table is a[ached to a mass m2 = 0.16kg. The length of string from the hole to m2 is 0.25m and the mass on top is rota+ng around the hole at the proper speed for the system to be in equilibrium. What is its linear speed? Angular speed?


Problem 9* A dumbbell consists of two balls, one of mass M and the other of mass 2M, connected by a light rod of length L. The dumbbell is mounted ver+cally on a pivot with the heavier ball at the bo[om. The pivot is located at the midpoint of the rod. The system, which is ini+ally at rest, is free to rotate about the pivot. A wad of pu[y of mass M and ini+al velocity V collides with and s+cks to the lower mass, as shown in the diagram. In terms of the quan++es given, what is the minimum value of V for which the dumbbell will make it all the way around.

L

V

X pivot


Problem 9* -‐ cont.

L

V

X pivot


Problem 11*

A cylinder of mass M and radius R is in sta+c equilibrium as shown in the diagram. The cylinder rests on an inclined plane making an angle θ with the horizontal and is held by a horizontal string a[ached to the top of the cylinder and to the inclined plane. There is fric+on between the cylinder and the plane. What is the tension in the string T?

!

T

M R


Vote for the problem you want me to work out

A)  Problem 1 – cars colliding (conservaMon of momentum)

B)  Problem 2 – moving center of mass and two parMcles (CoM)

C)  Problem 7 – two disks (conservaMon of angular momentum)

D) Problem 10 – pencil leaning on a wall (staMc equilibrium)

E)  Problem 12 -‐ bar with cables and an extra weight (staMc equilibrium)

Problem 1

Two cars collide at an intersec+on. Car A, of mass 2000 kg, is moving from west to east, while car B of mass 1500 kg, is going from north to south at 15.0 m/s. As a result of this collision, the two cars become enmeshed and move as one a]erword. A]er the collision, the enmeshed cars moved at an angle of 65° south of east from the point of impact. a) How fast were the enmeshed cars moving just a]er the collision? b) How fast was car A going just before the collision?


a)  vf = 7.09 m/s b)  vAi = 5.24 m/s

Problem 2 A system consists of two par+cles. At t = 0 one par+cle is at the origin; the other with a mass of 0.50 kg is on the y-‐axis at y = 6.0m. At t = 0 the center of mass is located at y = 2.4m. The velocity of the center of mass of the system is given by a) Find the total mass of the system. b) Find the accelera+on of the center of mass at any +me t. c) Find the net external force ac+ng on the system at t = 3.0s


!vCM = (0.75ms3)t2 i

Problem 7 Two disks are mounted on fric+onless bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, which has a mass of 1.00 kg and radius of 2.00 m, is set spinning at 45.0 rad/s. The second disk, which has a mass of 2.00 kg and a radius of 3.00 m, is set spinning at 25.0 rad/s in the opposite direc+on. They then couple together. What is their angular speed a]er coupling?


ωf = -‐12.3 rad/s

Problem 10

A picture below shows a pencil with its sharpened end res+ng against a smooth ver+cal surface and its erase end res+ng on the floor. The center of mass of the pencil is 9.00 cm from the end of the eraser and 11.0 cm from the +p of the lead. The coefficient of sta+c fric+on between the eraser and floor is m = 0.800. What is the minimum angle θ the pencil can make with the floor such that it does not slip?


tan! = 9cm.8(20cm)

! = 29.4!

Problem 12

A 350N, uniform, 1.50m bar is suspended horizontally by two ver+cal cables at each end. Cable A can support a maximum tension of 500.0N without breaking. Cable B can support up to 400.0N without breaking. You want to place a small weight on this bar. a) What is the heaviest weight you can put on the bar without breaking either cable? b) Where should you put this weight?


a)  ωmax = 550N b)  L = .614m from TA

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