REVIEW/DIAGNOSTIC HOMEWORK, PHYSICS 4304, Dr. Charles W. Myles
Due, Friday, January 28 in my mailbox or office by 5pm!
These problems are taken from exams of Physics 1403 (General Physics I) in recent semesters. The purpose of this is to FORCE YOU to review elementary mechanics material! Yes, there are a lot of problems & yes some are tedious. However, if you have trouble with these, chances are you'll have difficulties in the rest of the course & I wonder whether you should be in this Senior course! If this gives you difficulties, I strongly suggest that you seriously consider dropping this course & taking it again when it's next offered. Working on this is a good time to form Study Groups to collaborate on homework. Its easier to learn stuff with friends' help! If you don't have friends in class, make some! This is how physicists (& all scientists) work in “real life”. NO CONSULTATION with people who had this course previously & NO use of problem solutions posted in previous years is allowed! Any cheating will be dealt with harshly! Problem solutions (.jpg format) will be posted on the Homework Web Page shortly after the due date.
INSTRUCTIONS: PLEASE write on one side of the paper only!! PLEASE don’t write on the problem sheets, there won’t be room! PLEASE show all of your work, writing down at least the essential steps in the solution of a problem. Partial credit will be liberal, provided that essential work is shown. Organized work, in a logical, easy to follow order will receive more credit than disorganized work. The setup (PHYSICS) of a problem will count more heavily in than the detailed mathematics of working it out. PLEASE clearly mark your final answers & write neatly. If I can’t read your answer, you can't expect me to give it the credit it deserves and you are apt to lose credit. Each problem is equally weighted.
1. Answer these conceptual questions briefly, in complete, grammatically correct English sentences.
a. Using a ball thrown straight up into the air as an example, explain the error in the common misconception that acceleration and velocity are always in the same direction.
b. Explain the error in the common misconception that an object thrown upward has zero acceleration at its highest point.
c. See figure. A hockey puck is sliding at constant velocity across a flat, horizontal, frictionless ice surface. Which of the sketches in the figure is the correct free body diagram for this puck? Explain your answer using Newton’s Laws!
2. Answer these conceptual questions briefly, in complete, grammatically correct English sentences. You may supplement these sentences with equations, but keep these to a minimum!!
a. The first figure shows 2 water slides of different shapes. Starting at the same height
h, Paul & Kathleen start from rest at the same time on the two slides, which are
frictionless. Who is traveling faster at the bottom? What physical principle did you
use to answer this question? Who gets to the bottom first? Why?
b. In the second figure, the round objects are rolling without slipping down an inclined
plane of height H above the horizontal. The box is sliding without friction down
the slope. All round objects have the same radius R & the same mass M, which is
also the mass of the box. The moments of inertia for the round objects are: Hoop:
I = MR2, Cylinder: I = (½)MR2, Sphere: I = (2MR2)/5. The 4 objects are released,
one at a time, from the height H. Which one arrives at the bottom with the greatest
speed? Why? Which arrives with the smallest speed? Why? What physical principle
did you use to answer these questions? (You may write an equation here, but explain
the meaning of the symbols. I want most of the answer to be given in WORDS, not symbols!)
3. See figure. A cannon ball is shot from ground level towards a target. Its initial velocity is v0 = 125 m/s at an angle θ0 = 37º with the horizontal. Neglect air resistance.
a. Compute the horizontal & vertical components of the initial velocity.
b. Compute the maximum height of the cannonball. Compute the time it takes to reach this height.
c. Compute the time it takes to hit the ground. Compute the horizontal distance from its starting point where it hits.
d. Compute its height & horizontal displacement after it has been in the air for 10 s.
e. Compute its velocity (magnitude and direction) after it has been in the air for 10 s. (Alternatively, compute its horizontal & vertical components of velocity after it has been in the air for 10 s.)
4. See figure. A box of mass m = 20 kg is given a shove across a horizontal surface & then released at the origin with initial velocity v0 = 15 m/s in the positive x direction. After it is released, the only horizontal force on the box is friction between the box and the surface, which causes it to slow down and eventually come to rest. The coefficient of kinetic friction between the box and surface is μk = 0.25.
a. Draw the free body diagram for the box, properly labeling all forces.
b. Compute the box’s weight & the normal force between it and the surface.
c. Compute the frictional force the box experiences as it slides across the surface. What is the direction of this force?
d. Compute the acceleration (magnitude and direction) experienced by the box as it slows down. What force causes this acceleration?
e. How far from its release point will the box go before coming to rest? How long will it take to stop?
5. See figure. Two masses (m1 = 10 kg & m2 = 12 kg) are connected by a massless cord & placed on a horizontal, frictionless surface. The two-mass system is pulled to the right by a force FP = 40 N using a cord that makes an angle of 30˚ with the horizontal. The masses remain on the horizontal surface; there is no vertical motion.
a. Draw the free body diagrams for the two masses, properly labeling all forces.
b. Compute the horizontal & vertical components of the applied force FP.
c. Compute the normal force between mass m1 & the horizontal surface? (Hint: Does the normal force equal the weight?)
d. Compute the acceleration of the system.
e. Compute the tension FT in the cord between the two masses.
6. See figure. A planet, mass m = 1 ´ 1025 kg, is in a circular orbit at constant speed around a star, which is assumed to be a uniform sphere of constant density. The radius of the orbit (measured from the star’s center) is r = 1.5 ´ 1011 m. The mass of the star is M = 3 ´ 1030 kg. The gravitational constant is G = 6.67 ´ 10-11 N m2/kg2.
a. The planet goes around the star in a circular orbit, so obviously it experiences a centripetal acceleration. Using words (not equations!) tell me what the cause of this centripetal acceleration is. (Hint: See part b!)
b. Compute the gravitational force of attraction between the planet & the star. What is the “centripetal force” on the planet? (Hint: Answers to a & b should be consistent! You don’t need to know the speed of the planet to answer this!).
c. Compute the centripetal acceleration experienced by the planet. What is the direction of this acceleration? (You don’t need to know the speed of the planet to answer this!).
d. Compute the speed of the planet in orbit. Hint: Einstein taught us that the maximum velocity possible for any object is the speed of light, c = 3 ´ 108 m/s. So, if you get a velocity larger than this (or even a significant fraction of c!) YOU’VE DONE SOMETHING WRONG!
e. Compute the period of the planet’s orbit. Hint: This should be a time which is reasonable for the period of a planet orbiting a star, say, a time comparable to an Earth year! So, if you get a period very much larger than this (say millions of years!) or very much smaller than this (say a few minutes or smaller!) YOU’VE DONE SOMETHING WRONG!
7. See figure. The pulley has mass M = 10 kg and radius R = 0.5 m. It is a uniform solid disk with moment of inertia I = (½)MR2. A massless cord is wrapped around it & a tension force FT is applied. It starts from rest. After FT is applied for 10 s, the angular speed is ω = 50 rad/s.
a. Compute the pulley’s angular acceleration. Compute the linear (tangential) acceleration of a point
on the rim of the pulley.
b. Compute the net torque acting on the pulley. What physical principle did you use to do this calculation?
c. If FT is the only force producing a torque, calculate FT.
NOTE: The answers to parts d & e do not depend on the answers to a, b, & c!
d. After FT is applied for 10 s, compute the pulley’s kinetic energy & angular momentum.
e. After FT is applied for 10 s, compute the linear velocity & the radial (centripetal) acceleration of a point on the rim of the pulley.
8. See figure. A railroad engine, mass M = 50,000 kg, traveling at a speed of 20 m/s strikes a car, mass m = 5,000 kg, which is at initially at rest because it is stuck in the crossing (the people in the car have run away from it!). After the collision, the railroad engine & the car STICK TOGETHER and move off down the tracks.
Before Collision After Collision
a. Compute the initial momentum & kinetic energy of the engine.
b. Compute the momentum of the engine-car combination as they moved away from the collision. Compute their speed immediately after the collision. What physical principle did you use to find these?
c. Compute the kinetic energy of the engine-car combination immediately after the collision. Was kinetic energy conserved? Was momentum conserved? Explain (using brief, complete, grammatically correct English sentences!). Hint: It is physically impossible for the kinetic energy to INCREASE in such a collision!
d. Compute the impulse was delivered to the car by the engine. If the collision time was Δt = 2 x 10-2 s, compute the average force exerted by the engine on the car.
e. After the collision, the engine-car combination skids until it stops a distance d = 50 m away from the collision point. Assuming that work by the frictional force between the engine-car combination & the track is what causes them to stop, compute the work is done by friction in this process.
9. See figure, which shows a roller coaster car, mass m = 2,500 kg, on a portion of a roller coaster ride. The height difference between points A & B is 30 m. The height difference between points B & C is 25 m. The car starts from rest at point A. Take the zero of gravitational potential energy (y = 0) to be at point B. For parts b. & c. assume that the roller coaster track is frictionless.
a. Compute the gravitational potential energy of the car at points A, B, & C.
b. Compute the kinetic energy of the car at point B? Compute its speed there. What physical principle did you use to do this calculation?
c. Compute the kinetic energy of the car at point C. Compute its speed there.
d. Parts b. & c. assume that the track is frictionless. However, the measured speed of the car at point B is found to be vB = 20 m/s. This is less than the speed that you (should have) computed in part b. This means that friction cannot be neglected. In this case, compute the work done by friction when the car moves from point A to point B. What physical principle did you use to compute this work?
e. If the total distance traveled from point A to point B is d = 200 m, use the results of part d. to compute the frictional force acting on the car.
10. See figure. Two masses (m1 = 10 kg & m2 = 20 kg) are connected by a massless cord over a massless, frictionless pulley as shown. The masses are released, so that m1 moves upward & m2 moves downward.
a. Draw the free body diagrams for the two masses, properly labeling all forces. Don’t forget the weights, which are not shown in the diagram!
b. The two unknowns are the acceleration, a, of the masses & the tension, FT, in the cord. By applying Newton’s 2nd Law to the two masses, find the two equations needed to solve for a & FT.
c. Using the equations from part b, calculate a and FT (in any order).
11. See figure. A toy gun uses an ideal, stiff spring to shoot balls. The spring constant is k = 250 N/m. Neglect the ball’s gravitational potential energy in parts a., b., and c.
Before shooting After shooting
a. When the gun is cocked, the spring is compressed a distance x = 0.15 m. Compute the elastic potential energy of the spring when the gun is cocked.
b. If the gun shoots a ball of mass m = 0.25 kg, compute its kinetic energy just after it leaves the barrel. What physical principle did you use to find this result?
c. Compute the speed of the ball just after it leaves the barrel.
d. Assume that, after leaving the barrel, the ball is initially traveling horizontally at the speed computed in part c. If it is fired from a height h = 2 m above the ground (taking y = 0 as the ground level), compute its gravitational potential energy at that point. Compute its total mechanical energy at that point.
e. As the ball travels past the initial point discussed in part d., it falls to the Earth, some horizontal distance away. Compute the kinetic energy of the ball just before it hits the ground. Compute its speed at that same point.
12. See figure. Use energy methods to solve this problem!!! You will receive NO credit for using force methods! You don’t need to resolve forces into components to solve this!! A block, mass m = 35 kg, slides across a frictionless horizontal surface & up on to an inclined plane. The incline angle is 37º with respect to the horizontal. At the bottom, the mass has velocity v = 12 m/s. The mass moves up the plane & stops at a height H above the horizontal surface.