apps-dso.sws.iastate.edu · Web viewThe bottom disk #1 in the figure below with moment of inertia I1 = 10.0 kg·m2 is freely spinning about its symmetry axis at initial angular speed

SI Leader: KevinProfessor: Adhikari/Biswas

Spring 2015

Physics 221 Exam Review Sheet 1: Lectures 1-12

SI Leader: Kevin Houlihan

(Units, Vectors, 1-D Motion, Projectile Motion/ 2-D Motion, Circular Motion, Relative Motion, Newton’s First and Second Laws, Newton’s Third Law, Friction/Circular Motion Dynamics)

1. Dimensional Analysis (Dimensional analysis is basically a back check to make sure units are consistent.)

a. If there are 22.4 L of oxygen in 1 mol. And a single tank can hold up to 43 L of oxygen, if oxygen is 15.99 g/mol. How many grams will fit in one tank?

2. Vectorsa. Using what you know about polar coordinates, solve for θ, r, and │A│, if Ax =

3, and Ay = 4. (hint: r=|A|)b. Dot product is represented by A _ B and is a vector/scalar (circle one). Another

way to represent this is │A││B│_____θ. And another way is AxB_ + AyB_ + Az_____.

i. Acos θ is the projection of A onto B, so if the two vectors are perpendicular to one another, the dot product is _________.

ii. If the θ between A and B is 36 degrees, and Ax = 3, Ay =6; Bx = 5, By=2. What is the dot product of the two?

c. Cross Product is represented by A _ B and is a vector/scalar (circle one). Crossing these vectors gives us a third vector that is perpendicular/parallel (circle one) to the original two.│A x B │= │A││B│_________. Using the right hand rule if A points in the negative x direction and B points in the positive y, which direction does the cross product point?

3. 1-D MotionDetermine the acceleration (in m/s2) of an object which ... .

a. moves in a straight line with a constant speed of 20.0 m/s for 12.0 secondsb. changes its velocity from 12.1 m/s to 23.5 m/s in 7.81 secondsc. changes its velocity from 0.0 mi/hr to 60.0 mi/hr in 4.20 secondsd. accelerates from 33.4 m/s to 18.9 m/s over a distance of 109 m

4. 2-D Projectile Motion A tank fires a missile at a velocity of 240 m/s and at an angle of 35 degrees off a cliff that is 320 m high. (a) How far, horizontally, does the missile fly before hitting the ground below? (b) With what velocity (magnitude and direction with respect to the vertical) does the missile hit the ground?

5. Circular MotionA roller coaster car loaded with passengers, has a mass of 500 kg; the radius of curvature of the track at the bottom point of a dip is 12 m. The vehicle has a speed of 18 m/s at this point.

a. In the space below, draw a free-body diagram for the car (label forces according to type).

b. Calculate the acceleration and the net force acting upon the car. c. Calculate the force exerted on the vehicle by the track?


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6. Relative MotionA swimmer heads directly across a river, swimming at 1.6m/s relative to still water. She arrives at a point 40m downstream from the point directly across the river, which is 80m wide.

a. What is the speed of the river current? b. What is the swimmer’s speed relative to the shore?’ c. In what direction should she head so as to arrive at the point directly opposite to h

er starting point?7. Newton’s First and Second Laws

Two people are pulling on a box with Forces F1 and F2. Let θ1=20°,θ2=40°, mbox=5.0kg and a=1.1m/s2. What is the magnitude of the forces (F1 and F2)?

8. Newton’s Third LawA block of mass M = 5.0kg on an incline is attached to a rope that goes through a pulley on top of the incline. A counterweight of mass m is attached to the other end of the rope. The incline makes an angle θ=30 degrees with the horizontal. The coefficients of kinetic and static friction between the block and the incline are μs=¿0.30 and μk=0.40. The pulley and the rope are ideal and massless. The system is initially at rest.

a. Determine the maximum value of m (the mass of the counterweight) so that the block does not move up the incline. (4.2kg)

b. The string is cut so the block and the weight can move independently of each other. Find the acceleration of the block on the incline. (2.4m/s2)

9. Friction and Circular MotionThe maximum speed with which a 945-kg car makes a 180-degree turn is 10.0 m/s. The radius of the circle through which the car is turning is 25.0 m. Determine the force of friction and the coefficient of friction acting upon the car.

10. Apply the work equation to determine the amount of work done by the applied force in each of the three situations described below.


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11. A 40 g bullet moving with speed 330 m/s embeds itself in a wall, traveling 3.0 cm before it stops. (c) What was the power required to stop the bullet?



1. Olive Udadi is at the park with her father. The 26-kg Olive is on a swing following the path as shown. Olive has a speed of 0 m/s at position A and is a height of 3.0-m above the ground. At position B, Olive is 1.2 m above the ground. At position C (2.2 m above the ground), Olive projects from the seat and travels as a projectile along the path shown. At point F, Olive is a mere picometer above the ground. Assume negligible air resistance throughout the motion. Use this information to fill in the table.

2. Sheila (m=56.8 kg) is in her saucer sled moving at 12.6 m/s at the bottom of the sledding hill near Bluebird Lake. She approaches a long embankment inclined upward at 16° above the horizontal. As she slides up the embankment, she encounters a coefficient of friction of 0.128. Determine the height to which she will travel before coming to rest.

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4.

Position Height (m) PE (J) KE (J) TME (J) Speed (m/s)

A 3.0 0.0

B 1.2

C 2.2

F 0


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5. On the object below, locate the center of mass. (Choose Origin at center of 4x1 rectangle in center)

6. I release a solid cylinder and a hollow cylinder of equal mass so they both roll without slipping down a 30 degree incline ramp. If the vertical height of the ramp is 4 m, which cylinder will have more translational velocity at the bottom of the ramp? (You can do this with numbers but try to think about it quantitatively.) What are the final velocity of both cylinders?

7. The bottom disk #1 in the figure below with moment of inertia I1 = 10.0 kg·m2 is freely spinning about its symmetry axis at initial angular speed 10 = 20.0 rad/s. It is supported from below on an axle at its center like a merry-go-round. Now a stationary disk #2 with moment of inertia I2 = 8.0 kg·m2is dropped onto disk #1, and friction between the two disks causes the two disks to attain the same final angular velocity. The “system” consists of both disks. After dropping disk #2 onto rotating disk #1, it took 3.50 seconds for the two disks to reach the same final angular velocity.(a) What is the initial angular momentum of the system?(b) After disk #2 is dropped onto disk #1 and they attain the same angular velocity, what is this final angular velocity of the system?(c) What are the initial and final kinetic energies of the system? How much kinetic energy was lost after disk #2 was dropped onto disk #1? Where did the missing kinetic energy go?(d) What was the angular acceleration of each disk during this time?(e) What were the torques that each disk exerted on the other during this time?(f) How much work did each disk do on the other during this time? Use the Work-Energy Theorem to answer this question. What is the total work done on the two disks? How is this total work related to the kinetic energy lost by the system in part (c)?

8. Sir Lancelot is trying to rescue the Lady Elayne from Castle Von Doom by climbing a uniform ladder that is 5.0 m long and weighs 180 N. Lancelot, who weighs 800 N, stops a third of the way up the ladder. The bottom of the ladder rests on a horizontal stone ledge and leans across the moat in equilibrium against a vertical wall that is frictionless because of a layer of thick moss. The ladder makes an angle of 53.1° with the horizontal, conveniently forming a 3-4-5 triangle. (a) Find the normal and friction forces on the ladder at its base. (b) Find the minimum coefficient of static friction needed to prevent slipping at the base. (c) Find the magnitude and direction of the contact force on the ladder at the base. (d) If the actual coefficient of static friction at the base is 0.6, will Sir Lancelot make it to the wall or end up in the moat?

9. A tow truck is pulling a car out of a ditch with a cable which is 9.1 meters long and has a diameter of 1 cm. When the car begins to move the tension in the cable is 890 N. How much has the cable stretched? (Hint : You will need your equation sheet)(Ysteel =20*1010Pa)


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10. A satellite in circular orbit around Earth has a period of 3 hours. How far above the Earth’s surface is the satellite? (Mass of Earth is 5.97 x 1024 kg and radius 6.38 x 106 m.)



1. Consider the Energy curve shown below. If this system represents a mass m = 5 kg oscillating on a spring of spring constant k = 2,000 Nm. A mass is released from rest at the position x = 2 m. Determine the equation describing the motion of the mass.

2. (Damped Harmonic Motion) A rat of mass m is caught on the end of a spring with force constant

k. The rat is acted on by a damping force, F(t) = bv(t). a. What is the frequency of oscillation of the rodent?b. What value of bnew will cause the motion to be critically damped?

m = 300 g

k = 2.50 N/m

b = 900 g/s

3. ---------------------------------------4. What sound intensities

correspond to 28 dB and 92 dB?

5. What is the fundamental frequency (the lowest frequency harmonic) of an organ pipe 1 meter long? The organ pipe has one closed end and one open end. What is the third harmonic?

6. On a cold morning (say 5 degrees C) you fill your 15 gallon gas tank to the brim. (The volumetric coefficient of thermal expansion of gasoline is β=9.5×10−4 K-1 ) If the hottest


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temperature that day was 24 degrees C, how much gas would overflow out of your tank? (Assume that the change in volume of the tank is negligible).

7. One liter of water is at a boiling point when an unknown mass of ice at 0oC is added. If the final temperature is 30oC water, how much ice was added?

8.

9. If we take a balloon filled with nitrogen (N2) at room temperature (20 degrees C) with a volume of 32.1 Liters, if it is lowered to a temperature of -30 degrees C – what is its new volume?

10. The diagram below represents the Ericsson cycle, which works using isobaric and isothermal processes. If the the two pressure “reserviors” are at 1 atm and 0.3 atm and the initial volume is 1 L, how much work is done by this engine in one cycle? How much heat is released/absorbed? Assume that the cycle begins at room temperature and from 2 → 3 the cylinder is compressed down to 0.5 L

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Documents

apps-dso.sws.iastate.edu · Web viewThe bottom disk #1 in the figure below with moment of inertia I1 = 10.0 kg·m2 is freely spinning about its symmetry axis at initial angular speed