The Exam Consists of 6 Problems. Each Problem Is of Equal Value

Exam 1 S12 Phys 1210

______

your name

The exam consists of 6 problems. Each problem is of equal value.

You can skip one of the problems.

If you work all problems, I will count the best five grades toward the exam grade.

Tips for better exam grades :

Read all problems right away and ask questions as early as possible.

Make sure that you give at least a basic relevant equation or figure for each sub- problem.

Make use of the entire exam time. When you are done with solving the problems and there is some time left, read your answers over again and search for incomplete or wrong parts.

Show your work for full credit. The answer ‘42’ only earns you any credit IF ‘42’ is the right answer. We reserve points for ‘steps in between’, figures, units, etc. If all you give us is a numeric answer that may account only for a C grade for the problem in some cases.

No credit given for illegible handwriting or flawed logic in an argument.

All multiple choice questions may have more than one correct answer. For full credit, you need to mark all correct answers and mark no incorrect answer. 1. Kinematics, conceptual and numerical

a) Consider a vertical throw for which the object can land at a lower level than where it started. Assume that air resistance is negligible Hint: Use /g/ = 10 [m/s2]

Draw the vy-t diagram. Derive the y-t and ay-t diagrams by building the graphical

derivative and graphical integral of the vy-t diagram. Hint: Make sure to draw the time scales of each diagram such that a vertical line through all three diagrams connects points of equal time. b) If the maximum height is 20[m] above the launching height, what is the magnitude of the launch velocity?

c) If the launch velocity is 20[m/s], what will the velocity be at half the distance between launching height and the highest point? At which two times will the object be at this height?

2. Projectile Motion, conceptual and numerical

Consider a projectile motion without air drag where the projectile lands at the same height as where it had started (see figure). The launching velocity is 20[m/s] and the launching angle is 30 degrees.

Hint: Use /g/ = 10 [m/s2] and take downward as negative.

a) Draw the velocity and acceleration vectors and their components for each point shown in the y-x diagram below. Draw the vectors quantitatively to scale.

Draw the corresponding y-t and vy-t diagrams. Draw the curves quantitatively to scale.

b) Which statements about two-dimensional (x-y) projectile motion are correct?

A- Acceleration is constant B- At one point on the trajectory, the acceleration is zero C- Acceleration has only y component D- At some point on the trajectory the velocity vector is zero

E- When one doubles the mass of the projectile, leaving v0 and 0 the same, it will go less far in the x direction.

F- When one doubles the magnitude of the v0 vector of the projectile, leaving 0 the same, the projectile will go twice as far in x.

G- When one changes the launching angle 0 from 20 to 70 degrees, leaving v0 the same,

the projectile will go farther (xmax). H- At the point in the above diagram a dashed horizontal line connects two points of the trajectory. At these points, the magnitude of the velocity vector is the same.

c) What is the average velocity of the projectile between the two points at equal height, which are connected by the dashed horizontal line in above figure? d) Consider such a projectile that is launched at 30° with v0 = 20[m/s]. Suppose it hits a high vertical wall at x = 20[m]. At what height will it intercept the wall? What is its vertical velocity component at that time? What is the direction of the velocity vector at that time? 3. Kinematics and Vectors

An object of mass 0.5 [kg] is moving in the horizontal x-y plane. At t = 2[s] its position is Until then the object has been moving with a constant velocity

Hint: In the notation (+3, -4) the x-component of the vector has magnitude 3 and the y- component magnitude -4 in the units provided.

a) Find the position vector (magnitude and orientation) for t = 0.

b) At t= 2[s], suddenly a force (-2,+4) is exerted on the object, which is at that instant at location . Under this constant force, what will the velocity (magnitude and direction) be at t= 4[s]? c) At some point during the motion, vx=0. Where is the object when that happens? 4. Dynamics

Consider the normal Atwood Machine. The string and the pulley are massless and the pulley is frictionless. Both masses hang free without touching the ground when you release the system.

Hint: Air drag can be neglected. Use /g/ = 10 [m/s2]

a) Which of the following statements are correct? Use appropriate equations and vector drawings to support your reasoning below.

A- When two equal masses, A and B, are attached each to one end of the string, it is possible that the masses move at constant velocity.

Explain why:

B- When two unequal masses, A and B, are attached each to one end of the string, it is possible that the masses will not accelerate.

Explain why:

C- Two unequal masses are attached to the two ends of the string. When one doubles the larger mass, the resulting acceleration will double too.

Explain why: D- Two unequal masses are attached to the two ends of the string. When one doubles the mass of each of the two masses, the acceleration stays the same.

Explain why:

E- Two unequal masses are attached to the two ends of the string. When one doubles the weight of each of the two masses, the tension in the string stays the same.

Explain why:

b) Let the mass on the left side of a normal Atwood machine be 10 [kg] and the mass on the right side 11 [kg]. What is the acceleration of the lighter mass? What is the tension in the string?

c) The heavier mass starts with v0=0 at t=0 from 2[m] above the floor. At what time does the lighter mass reach its highest point?

5. Dynamics, numerical

A 2[kg] block slides on a taut massless string down an incline of 30°, which has a kinetic coefficient of friction of 0.2. The string may not be pulling parallel to the incline. The block slides with a constant velocity v = 2[m/s].

Hint: Use /g/ = 10 [m/s2].

a) Draw a free-body diagram of the block. Show all force components and define your x-y coordinates. Be qualitatively correct with your vector and component lengths.

b) Determine the magnitudes and directions for all forces. 6. Analyze a lecture video and apply lab skills and knowledge

A spring gun is used to launch two identical steel spheres to prove an important concept in free fall motion.

a) Describe the experiment and explain which concept is proven.

Support your reasoning by appropriate vector diagrams.

a) If you were to conduct this experiment in laboratory, explain how you would

decide whether the experiment was a success with regard to proving the principle dealt with in part a). Use proper statistical expressions and formulas to make your point.

b) Based on what you have learned in lab and pre-lab, identify two leading errors

apart from operator error, which would affect your experiment and discuss how the errors would affect the data. How could one minimize or eliminate these errors?

Master Equations – Physics 1210

One-dimensional motion with constant acceleration:

 find the other forms of master equation 1 by

(a) building the derivative of the equation

(b) solving the new equation for t and substituting it back into the master equation, and

(c) using the equation for average velocity times time

Two-dimensional motion with constant acceleration:



find the related velocities by building the derivatives of the equations

Newton’s Laws

find the related component equations by replacing all relevant properties by their component values

The quadratic equation and its solution: Need to take your mind of the exam for a second? Check this out:

A Few Interesting Facts About Newton

As a boy he showed little promise in school work. In fact, his school reports had described him as 'idle' and 'inattentive'.

Newton owned more books on humanistic learning and religion than on mathematics and science; all his life he studied them deeply and wrote about these topics.

He never married and lived modestly, but was buried with great pomp in Westminster Abbey.

He devoted much of his time to alchemy.

The final exam

There were two sophomores, who were going into the final physics exam. Before finals week they decided to go to a party and ended up staying longer than they planned, and they didn’t make it back for the final. They found the Professor after the final and explained to him why they missed it. They told him that they went up to Virginia for the weekend, and had planned to come back in time to study, but that they had a flat tire on the way back and didn’t have a spare and couldn’t get help for a long time. The professor thought this over and agreed that they could make up the final on the following day. The two guys were elated and relieved. The professor placed them in separate rooms and handed each of them a test. They looked at the first problem, which was something simple about projectile motion and was worth 5 points. “Cool” they thought, “this is going to be easy.” They did that problem and then turned the page. They were unprepared, however, for what they saw on the next page. It said: (95 points) “Which tire?”

So, there was this mathematician, physicist, and biologist who went into this building and counted to make sure it was empty, because it was set to be demolished. So they finish up and count and there is nobody inside. They go across the street and wait. After some time, two people enter. A few more minutes pass and three people exit. The physicist says “We must had miscounted”. The biologist says “They must have reproduced when they were in there”. The mathematician says “Alright, when one more person enters the building will be empty. Several scientists were all posed the following question: "What is 2 * 2 ?" The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99". The physicist consults his technical references, sets up the problem on his computer, and finally announces "it lies between 3.98 and 4.02". The mathematician cogitates for a while, then announces: "I don't know what the answer is, but I can tell you, an answer exists!".