Physics Exam 3

The fisherman knocks the tackle box overboard and it sinks to the bottom.

Falls

In the overhead view of the figure, a 400 g ball with a speed v of 8.5 m/s strikes a wall at an angle of 30° and then rebounds with the same speed and angle. It is in contact with the wall for 9.5ms. (a) What is the impulse on the ball (b) What is the average force exerted by the ball on the wall?

(a) mvsin(30)-(-mvsin(30)) (b) average force = impulse/t

A pellet gun fires ten 2.3 g pellets per second with a speed of 420 m/s . The pellets are stopped by a rigid wall. (a) What is the momentum of each pellet? (b) What is the kinetic energy of each pellet? (c) What is the average force exerted by the stream of pellets on the wall? (d) If each pellet is in contact with the wall for 0.90ms, what is the average force exerted on the wall by each pellet during contact?

(a) p = mv (b) KE= (1/2)mv^2 (c) Favg = p * 10/t (d) Favg = p/t

A set of crash tests consists of running a test car moving at a speed of 12.4 m/s into a solid wall. Strapped securely in an advanced seat belt system, a 73.0 kg dummy is found to move a distance of 0.810 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time. Using the direction of motion as the positive direction, calculate the average acceleration of the dummy during that time (in g's, with 1g = 9.81m/s2)

(a). W = deltaKE W = 1/2m(Vf^2-Vi^2) F = W/d (b). a = F/m (c). F = W/d

What are the coordinates of the center of mass of the three-particle system shown in the figure if m1= 9.0kg, m2= 6.0kg, and m3= 5.0kg?

(m1+m2+m3)x = m1x1 + m2x2 + m3x3 (m1+m2+m3)y = m1y1 + m2y2 + m3y3

An MSU linebacker of mass 110.0 kg sacks a UM quarterback of mass 89.0 kg. Just after they collide, they are momentarily stuck together, and both are moving at a speed of 3.30 m/s. If the quarterback was at rest just before he was sacked, how fast was the linebacker moving just before the collision?

m1u1 + 0 = (m1+m2)V

A cart of mass M1 = 4.00 kg and initial speed = 4.00 m/s collides head on with a second cart of mass M2 = 2.00 kg at rest. Assuming that the collision is elastic, find the speed of M2 after the collision.

m1u1 + m2u2 = m1v1 + m2v2 v2-v1 = u1-u2

A long thin rod lies along the x-axis. One end is at x= 1.00m and the other at x= 3.00m. Its linear density = 0.200x^2+0.500 in kg/m. Calculate mass of the rod. Calculate the x-coordinate of the CM of the rod.

m= Integral of density equation (from x=1 to x=3) x= (Integral of density*x) / m

A Princeton prof. (mass = 56.0 kg), surprised by the large stopping force he calculates for jumping flat footed from a height of 0.15 m, decides to try the experiment. Calculate he deceleration (in g's) if he stops in a distance of 0.44 cm.

v = sqrt(2gh) a = -v^2/2x

Flywheel The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.29 rad/s2. It accelerates for 25.9 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 57.1 s after it begins rotating.

w = at theta = w(t2-t1) theta = 1/2(wf-wi)t1 theta + theta = total angle

A bullet of mass m= 0.0300 kg is fired along an incline and imbeds itself quickly into a block of wood of mass M= 1.45 kg. The block and bullet then slide up the incline, assumed frictionless, and rise a height H= 1.20 m before stopping. Calculate the speed of the bullet just before it hits the wood.

1/2V^2 = gH v = [(M+m)/m] * V

A phonograph record on a turntable rotates at 33.333 rpm. What is the angular speed in rad/s? What is the linear speed of a point on the record at the needle at the beginning of the recording? What is the linear speed of a point on the record at the needle at the end of the recording? The distances of the needle from the turntable axis are 5.9in and 2.9 in at these two positions.

33.33 * (2pi)/60 v = wr for beginning: v1 = wr1 for end: v2 = wr2

The daughter gets in the water, looses her grip on the string, letting the balloon escape upwards.

Rises

The daughter pops the helium balloon.

Rises

The fisherman fills a glass with water from the pond and drinks it

Unchanged

The fisherman lowers himself in the water and floats on his back.

Unchanged

The fisherman lowers the anchor and it hangs one foot above the bottom of the pond.

Unchanged

A railroad flatcar of weight 7840 N can roll without friction along a straight horizontal track. Initially, a man of weight 596 N is standing on the car, which is moving to the right with speed 25 m/s. What is the change in velocity of the car if the man runs to the left so that his speed relative to the car is 8.0 m/s?

Vc(W+w) = uW + (u-Vm)w DeltaV = (u-Vc)

An old Chrysler with mass 2400 kg is moving along a straight stretch of road at 79 km/h. It is followed by a Ford with mass 1700 kg moving at 60 km/h. How fast is the center of mass of the two cars moving?

Vcom = (McVc + MfVf)/(Mc+Mf)

A shell is fired from a gun with a muzzle velocity of 23 m/s, at an angle of 60° with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that the air drag is negligible?

VoX = cos(60)*23 VoY = sin(60)*23 solve for t: 0= VoY - gt mVoX = 1/2mu tVoX + t(2VoX) = 3tVoX = distance

In the figure, wheel A of radius 10 cm is coupled by belt B to wheel C of radius 20 cm. Wheel A increases its angular speed from rest at a uniform rate of 1.8 rad/s2. Find the time for wheel C to reach a rotational speed of 100 rpm, assuming the belt does not slip

Wa = Wo + A(t) Va = Vc RaWa = RcWc

A point on the rim of a 0.55 m diameter grinding wheel changes speed uniformly from 9 m/s to 21 m/s in 6.3 s. What is the average angular acceleration of the wheel during this interval?

Wavg = (W-Wo)/t = (V-Vo)/(rt)

A bullet (m = 0.0270 kg) is fired with a speed of 92.00 m/s and hits a block (M = 2.80 kg) supported by two light strings as shown, stopping quickly. Find the height to which the block rises. Find the angle (in degrees) through which the block rises, if the strings are 0.530 m in length.

mv = MV KE = PE 1/2mV^2 = mgh h = L(1-cos(theta))

A proposed space station includes living quarters in a circular ring 50.5 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth?

mw^2r = mg (mass cancels) w^2r = g