Problem Set 1: Foundational Physics

Exam 1 Test Review Leader: Noah Session 3, week 4 Course: Phys 221 Supplemental Instruction Instructor: Canfield Iowa State University Date: 09/28/14

Notes: This version leaves no room for working the problems. Please bring notebook or similar paper to the exam review. Also note that this review should not be considered comprehensive, that is, we do not have enough time to review everything as a group.

Problem Set 1: Foundational Physics Units, dimensional analysis, order of magnitude estimates, significant figures, vectors, vector addition and multiplication, relative motion, frames of reference

1. What is the angle between the vector A=3i-2j-5k and the positive y-axis, in degrees?

2. An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 30.0 m/s due west during the flight, what direction must the plane fly relative to north to arrive at the destination?

3. Give (kk x 2î) ∙ (3ĵ).

4. The vector A is given by A = (6.0 m)î - (8.0m)ĵ . What is the unit vector A that points in

the direction of A?

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu 5. Let A = 3î - 5ĵ +2kk and B=î + bĵ k.+k Find b so the two vectors are perpendicular to one

another.

Problem Set 2: Simple Motion One and two dimensional motion, position/velocity/acceleration vs time graphs, constant acceleration, free fall, kinematic equations, projectile motion

1. A shopper needs to get to a store that is 1,200 meters to the north. The shopper walks the first half of the distance and runs the second half of the distance, taking a total time of 8.00 minutes. If the shopper’s running speed is three times her walking speed, what is the shopper’s walking speed?

2. The motion of an object is given by x(t) = 4.0t3 – 6.0t + 2.0, where x is in meters and t is in seconds. At what time does the object change the direction of motion?

3. A projectile is fired from point 0 at the edge of a high cliff with initial velocity components of vox = 60.0 m/s and voy = 175 m/s. The projectile rises and then falls into the sea. The time of flight of the projectile is 40.0 s, and it experiences no appreciable air resistance in flight. How high is the cliff?

4. A motorist traveling at a constant speed of 41.7 m/s in a 50 km/h speed zone passes a police car. Immediately after the car passes, the police car starts off in pursuit The police officer accelerates at 2 m/s/s up to a speed of 70 m/s and then continues at this speed until she overtakes the speeding motorist. How long from the time she started does it take the police car to overtake the motorist? The motorist continues at a constant speed during this process.

5. A ball is thrown straight up into the air in the positive y-direction. If the ball has an initial velocity of 20 m/s, find how long it takes for the ball to return to where it was thrown?

6. Which will have a greater in flight time, a projectile launched at 20 degrees, or a projectile launched at 60 degrees with respect to the horizontal? Assume that both projectiles have the same initial velocity.

7. The acceleration of gravity on the Moon is only one-sixth of that on Earth. If one shoots a cannonball on the Moon and a cannonball on the earth, both with the same initial speed and launch angle, what is the ratio of their ranges Rmoon/Rearth?

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu 8. On a position vs time graph, what does a negative slope indicate? What does concave up indicate?

9. What is indicated by the area under the velocity vs time graph?

Problem Set 3: Newton’s Laws Forces and resultant acceleration, action-reaction pairs, free-body diagrams, tension, normal force, pulleys

1. A block with mass 5.00kg is sliding down an inclined plane that is at an angle of 30.0 degrees with respect to the horizontal. In order for the block to slide down the inclined plane at a constant velocity, what must be the coefficient of kinetic friction between the block and the plane?

2. A worker is using the rope and pulley system shown below to lift the 35 kg mass upward with a constant acceleration of 4.0 m/s/s. If the ropes and pulleys are assumed to be massless, what tension does the worker need to create in the rope she is holding? (FIG 1)

3. Three boxes are stacked as shown below. A force F is applied to box B through a rope. Box C does not slip with respect to box B. Box A is attached to box B by a second rope. Box A has a mass of M and boxes B and C each have masses of 2M. Describe the net force on Box C in terms of the net force on A. (FIG 2)

4. A 12 kg lamp hangs from two light cables as shown. What is the tension in the left cable? (FIG 3)

5. A 3.0 kg book rests on a wooden incline that makes an angle of 10 degrees with the horizontal. The coefficient of static friction between the book and the incline is 0.3. What is the magnitude of the friction force on the unmoving book?

6. A 1.0 kg block is placed on top of a 4.0 kg block. The coefficients of friction between them are μk = 0.20 and μs = 0.30. The whole system is on a frictionless, horizontal table. A horizontal force F = 10 N is applied on the bottom block. What is the magnitude of the frictional force between the two blocks?

7. A box with a mass of 10 kg is suspended by a cable in an elevator that is moving up with an acceleration of 1.2 m/s2. What is the tension in the cable?

8. Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant acceleration a. Between which of the two blocks is the tension the largest?

Problem Set 4: Complex Motion Circular motion, friction, work, kinetic energy, power, springs, and simple spring modeling

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu 1. Two balls are rigidly attached to a disk that is rotating counterclockwise about its axis. Ball #1 is at a radius R from the center of the disk and Ball #2 is at a radius of 2R. The angular speed of Ball #1 is ω. What is the angular speed of Ball #2 in terms of ω?

2. The kinetic energy of a particle with mass m and speed v is K1. If m is halved and v is doubled, what is the new kinetic energy of the particle in terms of K1?

3. A spring has a constant k = 300 N/m. What is the amount of work done by an external force to compress the spring by 0.200 meters from its equilibrium length?

4. A 0.50 kg mass slides on a frictionless air track along the x-direction. When it first comes into contact with a spring, it has a velocity of 7.0 m/s. After compressing the spring by 20m/s, the velocity of the mass has decreased to 4.5 m/s. How much work has been done on the mass by the spring?

2 2 5. A force Fx = (3.0 N/m )x is applied on a particle as it moves along the x axis from the origin to x = 5.0 m. What is the work done by this force during this interval?

6. What is the magnitude of the acceleration of a point on the rim of a bicycle wheel (with radium equal to 40.0 cm) at t =1.50 s if the angular acceleration is given by α(t) = (4.00 rad/s3)t and the wheel is at rest at t=0.00s ?

7. A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12.0 meters. At what minimum rate must power be supplied to the sand mover?

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu FIG 1 FIG 2

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu