Nov 1, 2002
g=9.8 m/s2; Ffr=mFN; a*b= a b cosq; a x b= ab sinq; K=1/2mv2; Us=1/2kx2; Ug=Gm1m2/r ~mgh;
x-x0=v0t+ 1/2 at2; v=v0+at; vf2= vi2+2ad; S F=ma; t =r x F; St =I a; x=rq; v=rw; at=ra; ac=v2/r;

Multiple Choice: 3pts each
[1] A 4-kg cart starts up an incline with a speed of 3 m/s and comes to rest 2 m up the incline. The total work done on the cart is:
A) 6 J B) 8 J C) 12 J D) 18 J E) not enough information given

[2] A 50-N force acts on a 2-kg crate that starts from rest on a frictionless horizontal surface. At the instant the particle has gone 2 m (in how much time?), the rate at which the force is doing work is:
A) 2.5 W B) 25 W C) 75 W D) 100 W E) 1000 W

[3] The diagram below shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of stable equilibrium are:
U x a b c d e A) only a B) only b C) only c D) only d E) b and d

[4] A pendulum is constructed from a lightweight rod 0.50 m long attached to a weight. It is held horizontally and released from rest. At the lowest point in its swing, how fast will the pendulum be going?
A) 2.0 m/s B) 2.2 m/s C) 3.1 m/s D) 4.4 m/s E) 6.0 m/s

[5] A 80-kg hunter gets a rope around a 400-kg polar bear. They are stationary, 30-m apart, on frictionless level ice. When the hunter pulls the bear toward him, the polar bear will move:
A) 5m B) 6m C) 15m D) 24m E) 25m

[6] A student's life was saved in an automobile accident because an airbag expanded in front of his head. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter time. Compared to the windshield, the airbag:
A) causes a much smaller change in momentum B) exerts a much smaller impulse C) causes a much smaller change in kinetic energy D) exerts a much smaller force E) does much more work

[7] A 4-ton freight car moving at 3 mph bumps into a stationary 6-ton freight car. The two cars couple together. Their speed just after impact is:
A) zero B) 1.2 mph C) 1.9 mph D) 2.0 mph E) 3.0 mph

[8] Sphere A has a mass m and is moving with a velocity v. It makes a head-on elastic collision with a stationary sphere B of mass 2m. After the collision their speeds (vA and vB) are:
A) zero, v/2 B) -v/3, 2v/3 C) -v, v D) -2v/3, v/3 E) none of these

[9] Ten seconds after an electric fan is turned on, it is rotating at 300 rev/min. Its average angular acceleration is:
A) 3.14 rad/s2 B) 30 rad/s2 C) 30 rev/s2 D) 50 rev/min2 E) 1800 rev/s2

[10] String is wrapped around a 5.0-cm radius cylinder, which is free to rotate on its axis. If the string is pulled out at a constant rate of 10 cm/s and does not slip on the cylinder, the angular velocity of the cylinder is:
A) 2.0 rad/s B) 5.0 rad/s C) 10 rad/s D) 25 rad/s E) 50 rad/s

[11] The rotational inertia of a sphere about a diameter is (2/5)MR2, where M is mass and R its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:
A) MR2 B) (1/5) MR2 C) (2/5) MR2 D) (3/5) MR2 E) (7/5) MR2

[12] A disk with a rotational inertia of 5.0 kgm2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the rim. The angular acceleration of the disk is:
A) 0.40 rad/s2 B) 0.60 rad/s2 C) 1.0 rad/s2 D) 2.5 rad/s2 E) 10 rad/s2

[13] As the disk in problem 15 rotates through half a revolution, the work done by the force is:
A) 1.6 J B) 2.5 J C) 6.3 J D) 10 J E) 40 J

[14] A uniform disk, a hoop, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without slipping up identical inclines. Rank the objects according to how high they go, from least to greatest.
A)disk,hoop,sphere B)disk,sphere,hoop C)hoop,disk,sphere D)sphere,disk,hoop E)sphere,hoop,disk

[15] An ice skater with rotational inertia I0 is spinning with angular speed w0. She pulls her arms in, decreasing her rotational inertia to I0/3. Her angular speed becomes:
A) w0/ 3 B) w0/ SQRT(3) C) w0 D) SQRT(3) w0 E) 3w0

Homework-type Problems. Do any 3 of 4. Each problem is 18 pts.
[16] A satellite is in an elliptic orbit around the Earth as the above figure shows. Distance a=16,000 km, distance b=13,900 km. Its velocity at the perigee (perijove for Jupiter, periapsis in general) at point A is 8650m/s. Use conservation of energy to determine its velocity at point C, apogee (apojove, apoapsis, etc.)

[17] Before the Spanish Conquest, a tribe of Indians lived in the Mississippi valley that built their houses on mounds, possibly to avoid river floods. Consider a hemispherical mound that is 10 m high (it has a radius, R, of 10 m). An astute physics student notices that the radius in meters, r, of the circle formed by a horizontal plane cut through the mound is related to the height in meters, z, by the formula: r2 + z2 = 102. (a) How high is the center of mass? (b) If a cubic meter of soil weighs 2000 kg, how much work did these Indians expend in building this mound? Hint: the center of mass is found with this formula: ZCM = (1/M) INT z dm.

[18] A 0.30gm BB is shot into a 42gm foam pendulum suspended by 1.7m from the ceiling. If the pendulum is observed to deflect 13 cm to one side, how fast was the BB going?

[19] A hoop starts from rest on a magician's head and rolls without slipping over his ear, neck, shoulder and down his arm thereupon exiting his hand with horizontal velocity. If the magician is 2m tall, and his hand is 1m above the floor, how far from the magician will the hoop land? (Hint: find the velocity exiting his hand.)