PH 211 07-10-2015

Physics 211 Exam-3

NAME: _____________________________________ Write down your name also on the back of your exam.

SIGNATURE and ID: ___________________________ Return this hard copy exam together with your other answer sheets. Write down your name on the back of the package of sheets you turn in.

Show all your procedures when giving the answers to the questions

1. (33 points) In the figure below, block-2 of mass M= 1 Kg is at rest on a frictionless surface

and touching the end of an un-stretched spring whose spring constant is 200 N/m. The

other end of the spring is fixed to a wall. Block-1 of mass 2 Kg, travelling at speed v1 = 4 m/s,

collides with block-2 and the two blocks stick together. When the blocks momentarily stop,

by what distance is the spring compressed?

2. A 1 m long rod of mass m = 0.2 Kg is hinged at one end and connected to a wall. It is held

out horizontally , then released. With respect to the reference XY, whose origin is at the hinge (as shown in the figure), calculate:

(22 points) The speed of the tip of the rod at the moment it hits the wall?

(11 points) The kinetic energy of the rod at the moment it hits the wall?

vtip

X

Y

L= 1 m

Wall

3. 3A (17 points) Find the coordinates of the "Center of Mass" of the homogeneous thin plate

shown in the figure. Show all your calculations and the result.

X

Y

X

Y

Fig. 4a

Fig. 4b

O

4 cm

4 cm

O

1 cm

1 cm

1 cm

2 cm

3B (17 points) Find the coordinates of the "Center of Mass" of the homogeneous thin plate

shown in the figure. Show all your calculations and the result.

Optional (10 points, extra credit) A dictionary of mass M= 5 Kg is pushed against a vertical wall with a horizontal force of

magnitude F= 200 N, so that it does not slip down the wall, as shown in the figure. The

coefficient of static friction for the dictionary in contact with the wall is s = 0.3.

1A (2.5 points) Draw the free body diagram for the dictionary.

1B (2.5 points) Determine the magnitude of the normal force acting on the dictionary.

1C (2.5 points) Find the magnitude of the static friction force acting on the dictionary.

1D (2.5 points) If the magnitude of the force F decreases until the book is ready to slip, what is the magnitude of F when slipping is imminent?

Helpful formulas

Quadratic formula: ax2 +bx + c =0, 2a

acbb 2 4x

Average velocity = x / t instantaneous velocity v = d x / dt

Average acceleration = v / t instantaneous acceleration a = d v / dt

Motion under constatnt acceleration “a”

v = vo + a t

x - x o = vo t + (1/2) a t 2

v2 = vo2 + 2 a (x – x o)

Free fall

vy = voy - g t g = 9.8 m/s2

y - y o = voy t - (1/2) g t 2 x - x o = vox t g = 32 ft/s2

vy 2 = voy

2 - 2 g (y – y o)

Newton’s second law aF

m

Friction force

Ff = k N, Fs, max = s N _____________________________________________________________________________

Gravitational force near the Earth’s surface gF

m = constant; with g = 9.8 m/s2

Spring force x k -F

Work/Kinetic-energy theorem K = Wtotal

Work Wgravity-force fiW = - mg (zfinal – zinitial)

Work Wspring-force fiW = - (1/2) k [ (sfinal)2 - (sinitial)

2]

______________________________________________________________________________

Mechanical energy = kinetic energy + Potential energy

Center of mass

CMr

= ( i

mi ri ) / ( i

mi )

______________________________________________________________________________

Rotational motion v = R ______________________________________________________________________________

Rotational kinetic energy Krot = (1/2) I 2 ______________________________________________________________________________

Momentum of inertia I = i

mi ri2

Solid sphere of radius “R”: ICM = (2/5) M R2 (with respect to an axis passing through

though the CM)

Thin bar of length “L”: ICM = (1/12) M L2 (with respect to an axis passing through though the CM and perpendicular to the bar.)

______________________________________________________________________________

andres

Text Box

Optional quetion for extra credit