Quiz 1

A).  Coordinate Systems

To describe an object's motion quantitatively, we must first have a coordinate system.

A coordinate system is a collection of axes, each of which has an origin or zero point, and a positive and negative direction.  The dimension of the coordinate system is the same as the number of axes.

An object's position is its location relative to the origin of some coordinate system.  Position is a vector quantity, so it has both a magnitude and a direction (we will indicate vector quantities by using bold text).

In one dimension we can indicate the direction of a vector using + and -.  For now, we will consider one-dimensional motion and coordinate systems.

[One-dimensional coordinate line drawn pointing in a random direction, with a dot placed randomly upon it.  Same diagram as in Macintosh version.] 

In this one-dimensional coordinate system, is the position of the dot positive or negative?  

If wrong: Check the directions on the coordinate axis.  Positive is not always up and to the right; negative is not always down and to the left.


B).  Displacement

Displacement is the difference between arbitrary final and initial positions.  It is a vector quantity so it has a magnitude and a direction. 

Remember, in one dimension we can indicate the direction of the displacement vector using + and -.

[Coordinate line drawn randomly, with two points, P1 and P2, drawn randomly upon it.  Same diagram as in Macintosh version.]

Calculate the displacement between the initial position P1 and the final position P2.  Suppose each small tick mark represents one inch.  For example, if you thought the displacement was -1 inches, you would enter -1 inches.

If wrong: Be careful, Displacement = Final Position - Initial Position.  Also, check the directions on the coordinate axis; positive is not always to the right.



C).  Speed and Velocity

In physics, speed and velocity are not the same things.

Like displacement, velocity is a vector quantity with a magnitude and a direction.  Speed is a scalar quantity: it has no direction.  Speed is the magnitude of the velocity vector, so speed is never negative.

Physicists have precise, mathematical (and different!) definitions for each of the following:
			Average speed
			Average velocity
			Instantaneous speed
			Instantaneous velocity

(When we don't explicitly specify average or instantaneous, we mean instantaneous.)  Be sure you can distinguish amongst these terms.

[Train moving across the screen, with the distances and total time shown.  Train moves in more than one different direction so that total distance traveled isn't equal to the magnitude of the displacement.  Same diagram as the Macintosh version, same range of distances/times generated at random.]


a).  What was the locomotive's average speed (in miles/hour)?
b).  What is the magnitude of the average velocity (in miles/hour)?

Quiz 2


A).  Acceleration

When an object's velocity changes, it has been accelerated.  Since velocity is a vector, acceleration can be due to a change in the magnitude of the velocity (speed), or a change in the direction of the velocity.  

1).	A moving car slows to a stop to avoid hitting a brick wall...

	[Show movie.  Coordinate direction drawn at random.]

a).  With respect to the given coordinate system, was the car's velocity positive or negative?

b).  What about the acceleration?

2).	Now the car backs away from the wall with increasing speed...

	[Show movie.  Coordinate system same as before.]

a).  With respect to the given coordinate system, was the car's velocity positive or negative?

b).  What about the acceleration?


B).  Basic Trigonometry

Trigonometry will be a useful tool during your laboratory investigations.  The following questions will check your understanding of basic trigonometry.

You will need a calculator with trigonometric functions (sine, cosine, etc.) to answer these questions.

[Right triangle is drawn, with two of the following quantities (randomly chosen) known, the others unknown: Length of hypotenuse, length of adjacent side, length of opposite side, an angle.  Ask two of the following questions, based upon what is unknown.]

a).  What is the length of the hypotenuse?
b).  What is the angle (in degrees)?
c).  What is the length of the adjacent side?
d).  What is the length of the opposite side?


C).  Graphical Analysis

Understanding graphical analysis of motion is one of the key objectives of Lab 1.  The next few questions will check your grasp of some concepts you should understand before coming to lab.

[Position-time graph drawn for a motion consisting of steps of constant velocity motion.]

a).  What is the position (in meters) at t seconds?

b).  What is the speed (in meters/second) at t seconds?

c).  What is the average velocity (in meters/second) for the interval from time = 0 seconds to time = t seconds?

Quiz 3

A).  Scalars and Vectors

Some variables that we use to characterize a physical process depend on direction and some do not.  The quantities that give information about direction as well as magnitude are called vectors.  Those that only give information about the magnitude are called scalars.   Understanding the difference between scalars and vectors will allow you to solve physics problems correctly.

In the following questions, vector quantities will be indicated with bold type (unless you are being asked to specify if a quantity is a vector or a scalar).

Vector or Scalar?  Is  [random quantity (see below)] a vector quantity or a scalar quantity?

[List of random quantities:  
Scalars: distance, speed, average speed, time, a quantity with a magnitude but no direction.
Vectors: displacement, velocity, average velocity, acceleration, average acceleration, a quantity with both magnitude and direction.]


B).  Vector Components

A fast and convenient way of using vectors to solve a wide variety of physics problems involves resolving vectors into components.  Please answer the following questions about vector components.

[A vector is drawn randomly on a Cartesian coordinate system, the magnitude of the vector (in random units) and the angle between the vector and the x-axis or y-axis (chosen randomly) are both shown.] 

[Ask one of the following two questions at random]

a).  Please calculate the X component.
b).  Please calculate the Y component.








C).  Uniform Acceleration

In Lab 1 you investigated how gravity accelerates a cart on an inclined track.  Please use what you learned there to answer the following questions about the (frictionless) motion of a skier on a ski slope.

The skier accelerates down the slope, planting one of his poles once every half second.

[Movie of a skier accelerating down a ski slope is shown.  Same as Macintosh version.]

a).  Which of these pole tracks could represent the (frictionless) motion of the skier?  Please choose 1, 2 or 3.  [Same choices as in the Macintosh version.]

b).  If the top of the hill is the origin of the coordinate system, the time starts the moment the skier starts down the ski slope, and the positive position axis points down the hill, could this graph describe the [position/speed/acceleration, chosen randomly] of the skier?  [Answers: (c), (a), (h).]



Quiz 4


A).  Addition and Subtraction of Vectors

[Draw a coordinate system with the following ranges:  -5 < x < 5, -1 < y < 5.  Draw a vector of length A at an angle of qA degrees to the positive x-direction; draw a vector of length B at an angle of qB degrees to the negative x-direction.  A and B should each range randomly between 3 and 5 units in length, qA and qB should each range randomly between 20 and 70 degrees.  The angles and distances should be given. Label the vectors A and B.]

a)What is the magnitude of (A + B)?
b)What is the magnitude of (A – B)?

[Answers:  (a)  
(b) .]


B).  Acceleration of a Falling Object

We all know what happens when we drop a rock from the top of a building; the rock falls to the ground.  More specifically, the object accelerates towards the center of the Earth.  Near the Earth's surface, this acceleration is approximately constant (g = 32 ft/s2 or 9.8m/s2), thus we can use kinematic relations for constant acceleration to calculate the motion of a falling object.

A guard dog is on duty guarding a bank.

A robber appears suddenly, trying to steal a briefcase of money.

[Show movie as on Macintosh version.]

The robber intends to drop a 16-ton object from the top of the [H: 50ft<H<100ft] foot bank on the guard dog’s head...

The instant the robber drops the object, you yell to warn the guard dog.  If it is [H] feet above the guard dog’s head, how much time (in seconds) does he have to react?

[Answer:  seconds.]


C).  Tangential Velocity & Centripetal Acceleration

In this exercise, we will discuss the vector natures of both velocity and acceleration when objects undergo circular motion.  In particular, you will be using the mouse to draw the directions of the velocity and acceleration vectors on a planet in orbit about its sun...

You are watching from the top as a small planet orbits its sun.

[Show movie the same as that shown on the Macintosh version.]

a).  Draw a vector that could represent the velocity of the planet at its current position.  You do not need to be concerned with the length of the vector, just be sure the direction is correct.  [Answer: Tangent and forwards.]

b).  Now draw another vector that could represent the acceleration of the planet.  [Answer: Toward center of orbit.]



Quiz 5

A).  Forces

The solution of force problems often involves resolving forces into components.  In doing so we can determine the overall or net force on an object.  You already have experience with vector components from your work with projectile motion, so these next questions should serve as a review.

1).	[Random vector drawn on the screen on Cartesian coordinates.]

a).  Draw the X component of this force vector.
b).  Draw the Y component of this force vector.

Use the Draw - Vector OK [change this to whatever is appropriate on the new version] option at top of screen when satisfied with the vector component you've drawn.  The curved line between the rays indicates the angle.

2).	[Random vector drawn on the screen on Cartesian coordinates, the magnitude of the vector and its direction are shown.]

a).  Calculate the X component of this force vector.
b).  Calculate the Y component of this force vector.


B).  Force Components
		 
In this unit, we will explore the utilizations of force diagrams in force related problems.   The description section of the problem solving strategy prompts us to use both free-body and force diagrams in the analysis.  Press any key to see how these ideas can be successfully applied.

1).	[Picture of book shown.]

Draw the forces on the book.  As each is completed choose Vector OK from the draw menu [change this to whatever is appropriate on the new version].  [As this is done, student is asked to classify each force: weight, normal force, tension, or friction.]

Solving force problems requires the use of free-body and force diagrams.  Click on the book to isolate it and thus create the free-body diagram.

Once the forces are identified on the isolated body, we construct a "convenient" coordinate system with a point representing the object in question located at its origin.  Choose the system that has an x-axis perpendicular to the wall and the y-axis parallel. Click on the isolated book to continue.

Draw the forces on the force diagram. As each is completed choose Vector OK from the Draw menu located at the top of the screen [change this to whatever is appropriate on the new version].  [For each force, the relevant angle from the previous diagram is requested.]

2).	a). The book hangs midway between a stretched rope with total length of [L: 1.6m<L<3m] meters.  The distance between the supports is 1 meter.  Calculate the angle q [The angle between the rope and the horizontal.] in degrees.

[Answer: .]

b). The book has a mass of [M: 0.5<M<1.2] kilograms.  What is the force of the earth on the book?

	[Answer: Mg.]

c). Calculate the tension in the rope for a book of mass M.

	[Answer:  .]

d). What is the magnitude of the force exerted on the right wall?

	[Answer: Same as (c).]





Quiz 6


A).  Frictional forces

In any real situation in which one surface slides over another, there will be a frictional force acting on the object against its motion.  In some situations, for example the motion of a car on an air-track, the frictional force is small enough that it can be neglected; in other situations, such as those dealt with in Lab III Problem #3, #4, and #5, we need to take friction into account.

A block of mass [M: 1kg<M<5kg] is resting on a rough, level surface.  The coefficient of kinetic friction between the block and the surface is [mk: 0.2<mk<0.6]; the coefficient of static friction between the block and the surface is [ms: ms = mk + 0.1].

[Draw a block resting on a horizontal surface.]

a)What is the magnitude of the frictional force on the block? 
[Answer: zero.]

[Draw a horizontal rope pulling the block to the right, with the tension force marked in the rope.]

b)The block is now pulled to the right by a rope with a force of 
	[T: (9.8msM – 1) < T < (9.8msM + 1)] Newtons, does the block begin to move?
	[Answer: If (9.8msM) < T then yes, if T < (9.8msM) then no.]

c)The block is pulled to the right and accelerates with an acceleration of  [a: 3<a<7] m/s2, with what force is the block pulled?
[Answer: T = M(a + 9.8mk).]












B).  Force Diagrams, a Dynamical Case

As seen in the previous unit, the use of force diagrams provides us with a tool to solve complex problems in physics.  In this unit, we will explore the utilization of force diagrams as applied to a dynamical case, that is one in which the object in question is in motion with an acceleration that is constant.   Press any key to continue.

1).	A block is being pulled up a rough incline:

[A block is being pulled up a rough incline by a rope parallel to the slope.]

a).  Draw the force vectors on the block as if it were in motion up the rough incline.  As each is completed, choose Vector OK from the Draw menu located at the top of the screen [change to whatever the equivalent is in the new program].  [As each force is drawn, the student is asked to classify it: weight, tension, normal force, or friction.]

Once the free-body diagram is labeled, we choose a "convenient" coordinate system for the force diagram.  Consider the system with the x-axis parallel to the incline and the y-axis perpendicular to this.   Click on the block to continue.

Redraw the forces on the force diagram.  As each is completed choose Vector OK from the Draw menu.  For each force, the relevant angle from the previous diagram is requested.

b).  Which is applicable here, the coefficient of static friction or the coefficient of kinetic friction?  Answer with the letter s for static or k for kinetic.
Quiz 7


A).  Kinetic Energy and Work

Previously we saw an application of acceleration where free body and force diagrams along with Newton's second law of motion were used as tools to unravel the solutions to interesting physical problems.   However, there is an alternative technique to solving these problems, one based on the conservation of energy.  The questions in this part of the lab quiz use energy/force relations in an attempt to verify your understanding of the fundamental concepts of energy and forces.
	
1).	A Peregrine Falcon living in the skyscrapers of Minneapolis zeros in on an unsuspecting pigeon for dinner.  The falcon has a weight of [W: 4<W<10] pounds and is diving with a speed of [v: 30<v<220] miles per hour.  What is its kinetic energy?
(1 pound = 4.45 N, 1mile = 1609 meters) 

[Answer:  Joules.]

2).	A parachutist's velocity changes by a factor of [1/f: 3<f<20] when the parachute opens. His kinetic energy changes by a factor of 1/x, what is x?

[Answer: .]

3).	A car having a mass of [M: 900<M<1200] kg and traveling at v [5<x<25] m/s is stopped in x meters after running into some bales of hay.  What is the magnitude of the average force of the hay on the car?

[Answer: .]












B).  Average and Instantaneous Velocities

When an object is in motion it has associated with it an energy that is related to this motion and thus it is essential that you understand the difference between average velocity and instantaneous velocity.  The following questions will check your understanding of these concepts.

[Draw a data table giving horizontal and vertical components of position and velocity at times 0.0s, 0.2s, 0.4s, 0.6s, 0.8 s, 1.0s.  Same as Macintosh version.]

This data represents the horizontal and vertical components of position and velocity for an earth-body system.  Use the data to answer the following questions about this body.

[For each of the following questions, ask either part (a) or part (b).]

1).  Instantaneous velocity of component
a).  What is the horizontal component of the velocity at t seconds?
b).  What is the vertical component of the velocity at t seconds?

2).  Average velocity of component.
a).  What is the average horizontal velocity for the first t seconds?
b).  What is the average vertical velocity for the first t seconds?

3).  Instantaneous speed
What is the speed at t seconds?

4).  Average velocity magnitude 
What is the magnitude of the average velocity for the first t seconds?


Quiz 8


A).  Kinetic Energy and Work


1).	A pogo stick is fitted with a spring having a force constant of k N/cm.  Billy Bob's weight causes an x centimeter compression of the spring from its equilibrium position.  To do so, what energy transfer is required?




B).  Energy Efficiency of a Collision

According to the law of conservation of energy, energy can neither be created nor destroyed.  However, different forms of energy (e.g. kinetic energy, gravitational potential energy, thermal energy, and chemical energy) may be transferred to other forms of energy, as long as the total energy remains constant.  Therefore, conservation of energy doesn’t imply that the total kinetic energy of a system has to remain constant during a collision, but the degree to which kinetic energy is actually conserved in a collision is determined by its efficiency.

A rubber ball, of mass [m: 20<m<50] grams, was thrown against a wall at a speed of [v:1<v<6] m/s.  The energy efficiency of the collision was [G: 0.5<G<0.9].

1).	At what speed did the ball rebound?
	[Answer:  m/s].

2).	How much energy was dissipated in the collision?
	[Answer:   Joules.]


C).  Elastic and Inelastic Collisions

Classify each of the following collisions as elastic, inelastic, or perfectly inelastic. 

a)A ball is dropped on the ground and rebounds to [p: 10 < p < 80] percent of its original height. [Inelastic.]
b)A lump of clay is dropped on the floor, where it sticks and doesn’t rebound. [Perfectly inelastic.]
c)A rubber ball is thrown at an uneven brick wall and rebounds at a different angle but at exactly the same speed as before the collision.  [Elastic.]
d)A rubber ball is thrown at a brick wall and rebounds at exactly half its initial speed.  [Inelastic]
e)Two cars of exactly the same mass, initially moving at different speeds, collide and stick together.  [Perfectly inelastic.]



Quiz 9



A).  Scalars and Vectors

You must understand the difference between scalars and vectors if you hope to solve physics problems correctly.

The following questions check to see if you remember whether various quantities are vectors or scalars:

1).	Is  [random quantity] a vector quantity or a scalar quantity?


B).  Collisions

This unit will verify your understanding of some fundamental relationships used in conservation of momentum problems.

1).	A Peregrine Falcon living in the tallest of buildings in downtown St. Paul, zero's in on a an unsuspecting pigeon for dinner.  The falcon has a weight of W pounds and dives with a speed of v miles per hour.  What is its momentum?
(1 pound = 4.45 N, 1mile = 1609 meters.) 

2).	By stretching its wings open, the falcon having a mass of M kg undergoes a change of velocity of V m/s in t seconds in order to make the interception of its prey possible.  Is it true that the upward force caused by air resistance is f Newtons?  [f = mdv/dt = dp/dt]

3).	The falcon having a mass of M kg collides with an m kg pigeon in a perfectly inelastic collision. The falcon's initial velocity relative to the pigeon is u m/s.  Is the final velocity of the two birds v m/s?  [v=u*m1/(m1+m2)]

4).	A beam floating at u1 m/s toward a space station that is being assembled is grabbed by an m2 kg space mechanic.  The mechanic is moving rectilinearly toward the m1 kg beam with a speed of u2 m/s.   After grabbing the beam, what is their common speed?

5).	An M kg Volkswagon Superbeetle travelling at V m/s skids to a stop in a distance of x meters.  What is the magnitude of the frictional force causing it to stop?

6).	One can skip a Whamo 165 gram Frisbee off the concrete if thrown at an angle of q degrees measured from the ground.  In doing so the frisbee rebounds at the same angle but undergoes a velocity change of v m/s  when  interacting  with the ground for t seconds.  Is the average impeding force on the frisbee f Newtons? 
[f = mass.cosq.dv/dt]


C).  Conservation of Momentum 

In lab we have used air carts to explore the ideas of kinematic motion. In this week's laboratory we will use the carts to discover the ideas conservation of momentum and energy for both the elastic and inelastic type of collision.  So as to become comfortable with the content of this week's lab, answer the following questions:

1).	A moving car slows to avoid hitting a stalled bus but misjudges the distances and lightly bumps the bus. (No passengers are hurt.)

The car, weighing W1 Newtons, hits the bus with a speed of u km/hr and elastically rebounds with a speed of v km/hr.  With what speed did the bus initially rebound?  The bus has a weight of W2 Newtons.  Express your answer in units of km/hr.

2).	Now the car having momentum of P Ns hits the bus resulting in light damage to the front of the car.  The two vehicles undergo an inelastic collision with an impulse, due to friction, of J Ns that acts for a short time and in the direction opposite to the car's original motion; what was the common speed of the two vehicles after the short time that the impulse occurred?  The mass of the car is M1 kilograms, and that of the bus is M2 kilograms. Express your answer in units of km/hr.

3).	[Movie of the car colliding with a wall.]
The car's front end is smashed, it rebounds and skids to a stop in t seconds.  Find the speed of the car just after colliding with the wall if the coefficient of kinetic friction between the cars tires and the road is m. Express your answer in units of km/hr.

Quiz 10


A).  Tangential Velocity & Centripetal Acceleration

In this exercise, we will discuss the vector natures of both velocity and acceleration when objects undergo circular motion.  In particular, you will be using the mouse to draw the directions of the velocity and acceleration vectors on a planet in orbit about its sun...

1).	a).  You are watching from the top as a small planet orbits its sun....  Draw a vector that could represent the velocity of the planet at its current position.  You do not need to be concerned with the length of the vector, just be sure the direction is correct.

b).  Now draw another vector that could represent the acceleration of the planet.

2).	The Return to Planet X

The earth moves in a nearly circular path around the sun in one years time.  Any two masses exert forces of attraction on the other.  This force of attraction, referred to as the Gravitational Force, is responsible for the circular motion of the earth around the massive body, the sun. 

Consider an arbitrary planet, Planet X, which revolves about its sun at a constant speed with a period of T Earth days.  The radius of its circular orbit is R million kilometers....  (Express your answer using computer notation, e.g. 5.0E+24 instead of 5.0 x 1024.)

a).  What is the average speed for half an orbit (from position P1 to position P2) in kilometers/hour?  Note: The orbit is circular, we are watching from slightly above the plane of the orbit.

b).  What is the magnitude of the average velocity over the half orbit?  (Express your answer in kilometers/hour.)

c).  Assuming Planet X orbits at a constant speed, what is the magnitude of the instantaneous velocity (in kilometers/hour) at position P3 ?

d). If Planet X has a mass of M kilograms, what is the magnitude of the gravitational force that the sun exerts on Planet X?






B).  Rotational Kinematics

Rotating objects are often treated as rigid bodies (bodies which do not change volume or shape). When describing the rotation of a rigid body about an axis, we characterize the motion of the body by describing its angular position, angular velocity, and angular acceleration.  These quantities can be thought of as analogues of familiar ones from translational motion: position, velocity, and acceleration. 

1).	A horizontal disk of radius R centimeters rotates horizontally about its center. A point on the perimeter of the disk travels a distance of x centimeters in t seconds.
	
	a) Through what angle did the disk rotate?

	b) If the disk rotated at a constant rate, what was its angular speed?

2).	A horizontal disk of radius R centimeters rotates horizontally about its center.  The disk starts from rest and reaches an angular speed of w rad/sec t seconds later. 
	
	a) What was the angular acceleration of the disk?

	b) What was the total distance traveled by a point on the perimeter of the disk?























Quiz 11


A).  Moment of Inertia

The moment of inertia of a system of masses about a particular axis tells us how the mass is distributed around that axis.  The moment of inertia depends upon mass, how that mass is distributed, and also upon the axis about which it is being measured.  The moment of inertia is the rotational motion analog of mass in linear motion, except that it must be defined relative to some axis.

[Display a diagram showing three masses, m1, m2, and m3, which are respective distances d1, d2, and d3 from an axis shown.]

The diagram shows three masses that are free to rotate about the axis shown.  Calculate the total moment of inertia of the system of particles about the axis.


B).  Moment of Inertia about Different Axes

The moment of inertia of a body about an axis depends both upon the distribution of mass in that body and upon the axis about which the moment of inertia is being measured.  The axis must always be specified, or the moment of inertia is meaningless.

[Draw a picture of an object with three parallel axes drawn through it.  Axis 2 passes through the center of mass, which is labeled on the diagram.  The other axes are perpendicular distances a and b from axis 2.]

The object above, of mass M kg, has a moment of inertia of I1 about axis 1, what is its moment of inertia about axis 2?  

What is its moment of inertia about axis 3?












C).  Torque

In order to cause an object to experience a linear acceleration, you must exert a force on that object.  Similarly, in order to cause an object to experience an angular acceleration, you must apply a force to the object in such a way as to affect its rotation.  This angular acceleration is affected not only by the force itself, but also by the position it is applied to the object relative to the axis of rotation.  

A wheel of radius R meters is free to rotate about its central axis; its moment of inertia about this axis is I.  

a).  A force of magnitude F Newtons is applied tangentially to the wheel, calculate the magnitude of the torque produced by this force about the central axis of the wheel.

b).  If there are no other forces acting on the wheel, calculate the angular acceleration of the wheel.






Quiz 12


A).  Kinetic Energy of Rotation

A body that is in translational motion has some amount of kinetic energy dependent upon its mass and the speed with which it is moving.  Similarly, a body in rotational motion has kinetic energy.  We can divide the body into small elements of mass, each of which is moving at a different speed.

[Draw a diagram of a hoop with the axis through its central axis shown.]

The hoop in the diagram rotates about its central axis at a constant angular speed w.  The hoop has a radius R meters and a total mass M kg.

a).  What is the moment of inertia of the hoop about its central axis?
b).  What is the kinetic energy of rotation of the hoop?


B).  Angular Momentum

As it is useful to define the linear momentum of an object to help understand its motion, and to consider changes in linear momentum to be the result of external forces, so it is useful to think of the angular momentum of an object.  And, likewise, to consider the conservation of angular momentum.

1).	You are watching as an observation satellite revolves around the moon: The satellite has a mass of M kg.  It orbits x km above the moon's surface.  Each orbit takes t minutes.  The radius of the moon is 1738 km.

a).  What is the magnitude of the angular velocity of the satellite in radians per second?

b).  What is the moment of inertia of the satellite in kilogram-meters squared?

c).  What is the angular momentum of the satellite in kilogram-meters squared per second?

[HINT: Treat the satellite as a point particle.]




Quiz 13