EXAMPLE QUESTIONS:
Listed below are some basic questions that cover each of the learning goals for the course so far. Many more examples can be found in the text.
REPRESENTING MOTION

• Represent the motion of an object using a motion diagram, a position versus time graph, a velocity versus time graph, or an acceleration versus time graph. 

1) A block with some initial velocity slides on a frictionless surface. Draw a motion diagram for the subsequent motion, and make graphs of position vs time, velocity vs time, and acceleration vs time.

2) Do the same for the x position,velocity and acceleration of a block sliding on the frictionless track below:


3) Do the same for the y position of an dropped object that eventually reaches terminal velocity

• Qualitatively describe the motion of an object given one of these representations of its motion.

4)  Give a description (in words) of the motion of an object whose position vs time graph is the one shown below:



5)  Give a description (in words) of the motion of an object whose velocity vs time graph is the one shown above.

6)  Give a description (in words) of the motion of an object that starts at rest and whose acceleration vs time graph is the one shown above:

• Translate between graphs of position versus time, velocity versus time, and acceleration versus time  

7) If the graph above represents velocity vs time and the object starts at position 0, draw the acceleration vs time graph and the position vs time graph.

• Provide a mathematical description of an object's motion by introducing a set of coordinates and giving the position as a function of time, (x(t),y(t),z(t)).

8) For the situation in question 2, give a mathematical description of the motion.

• Identify the magnitude and direction of position, velocity, and acceleration for a moving object at a particular time given some description of its motion.

9) A ball's position as a function of time is (-5 m/s³) t³. What is the location, velocity, and acceleration of the ball at t = 2s?

10) The position of a ball is given by the graph in question 4, where the initial and final positions are 10m and 20m and the change happens between 4s and 6s. What are the position, velocity and acceleration at 5s? 

• Explain the difference between average and instantaneous velocity

11)  In the position vs time graph below, which is greater, the instantaneous velocity at 5s or the average velocity between 0 and 5 s.



12)  In the position vs time graph above, the function is a parabola and the position at 5s is 1m (the position is 0 at time 0). What is the instantaneous velocity at time 5s, and what is the average velocity between 0 and 5s?

• Calculate average or instantaneous velocity and acceleration numerically using position vs time data 

13) The data below represent the position of an object at times 0,0.01s,0.02s,0.03s,0.04s,0.05s,0.06s,0.07s,0.08s,0.09s,0.1s. Estimate the instantaneous velocity and acceleration at time 0.05s.

4m,4.02m,4.08m,4.18m,4.32m,4.50m,4.72m,4.98m,5.28m,5,62m,6m

MOMENTUM CONSERVATION

• Calculate the momentum of a moving solid object or the total momentum of a collection of objects, adding vector components where necessary

13.5) A 1 kg ball moves at speed 10m/s in a direction 30 degrees above the horizontal. A 2kg ball moves toward it at speed 30m/s in a direction 45 degrees above the horizontal. Calculate the horizontal and vertical components of the total momentum.

• Explain how mass can be defined without gravity 

13.6) Describe an experiment that can be used to determine the relative mass of two objects in outer space (where we can't just weigh them).

• Explain how momentum conservation leads to Newton's first law

14)  Using conservation of momentum, prove Newton's first law.

• Explain how momentum conservation may be used to predict the location of an isolated object at a future time given its position and velocity at some initial time

15) An object in outer space is moving in the x direction. If it is initially at x=2m and has initial velocity 5m/s, what is the position and velocity 10s later. Justify your answers using conservation of momentum.

• Evaluate whether a hypothetical collision process conserves momentum

16) A 1kg ball moving at speed 10m/s collides with a 3kg ball that is stationary before the collision. Which of the following is a possible outcome of the collision? (you would be given some choices here)

• Use momentum conservation to deduce initial or final velocites of objects in collisions problems in one, two or three dimensions.

17) In the previous scenario, original ball is stationary after the collision. What is the final speed of the other ball?
18) In the scenario of question 16, the balls instead stick together in the collision. What is the final speed of the pair of balls.
19) In the scenario of question 16, the first ball hits the second in a glancing collision and moves off with speed 5m/s in the direction 45 degrees from the direction of its initial velocity. What is the final velocity of the second ball (either find speed and direction or give x and y components).

• Explain how momentum conservation can be used to argue that the change in momentum will be the same for any two objects under the same external influence.

20) A block of wood and a block of gold of equal volumes sit on a frictionless surface. Tennis balls with equal mass and speed are thrown at each block, and the tennis balls are observed to bounce backward from the two blocks at equal velocity. Which block has the larger momentum after the collision. Explain your answer.
21)  The same two blocks are pushed with a force equivalent to 45 tennis balls per second bouncing off as in question 20. Will the rate of change in momentum be greater for the wood block or the gold block? Why?

• Describe the relationship between Force and Change in momentum (=impulse)

22) A car accelerates from rest to a constant velocity. Sketch a graph of the net force on the car as a function of time and the cumulative change in momentum as a function of time. How are these two graphs related?
23) In question 21, each tennis ball changes its momentum by 0.1 kg m/s in the collisions. What is the force felt by the blocks?   

• Qualitatively describe the force vs time and momentum vs time for some simple interactions (e.g. throwing a ball)

24) James throws a ball, which hits a wall and bounces back. Sketch a graph of the net horizontal force on the ball vs time and momentum (in the horizontal direction) of the ball vs time, ignoring air resistance.

• Explain how momentum conservation leads to Newton's Third Law

25) A system of two objects in outer space interact through a new 5th force. One scientist claims that the new force doesn't satisfy Newton's 3rd Law. Argue that this claim would violate momentum conservation. 

• Evaluate which components of momentum are conserved in specific situations

25.5) Which of the following momenta are conserved?

A) The horizontal momentum of a block sliding along a table with friction
B) The total momentum of two balls in an inelastic collision
C) The horizontal momentum of a ball sliding down a frictionless ramp.
DYNAMICS FROM NEWTON'S SECOND LAW

• To identify the forces acting on an object in various simple situations, to identify the magnitudes of these forces and draw a force diagram showing the directions of these forces(if they are from gravity, a spring, the normal force, friction, air drag, a rope).

26) Draw a force diagram and identify the magnitudes of the forces for:

A projectile moving through air with a drag force.
A block sliding down a ramp with friction
A block sliding down a ramp with friction, gravity, and air drag if the block is also connected to a post at the top of the ramp by a spring.

• To write the different component equations (for the x, y and z directions for some choice of coordinate axes) coming from Newton's second law for an object acted on by known forces.

27) A projectile moves with velocity (Vx,Vy) in a liquid for which there is a speed-independent drag force D opposite to the direction of motion. What are the x and y components of this force?
28) For the scenarios in question 26, write down the x and y components of the equations arising from Newton's second law, where x and y are along the horizontal and vertical directions.
29) Rewrite your equations in 28 in the form

dVx/dt = ...   dVy/dt = ...

• To explain why Newton's second law can be used to determine position and velocity of an object at future times given the initial position and velocity.

29) Explain why Newton's second law determines in prinicple the future positions and velocities of an object based on its current position and velocity, assuming all the forces on the object are known (as a function of its possible locations and velocities)

• To use equations of motion derived from Newton's second law to determine the approximate location of an object at a slightly later time given its position and velocity at the present time.

30) A ball is initially at X=3m, Y=0  with velocity 12m/s in the y direction and 0 in the x direction. If the equations coming from Newton's 2nd law are

dVx/dt = - 0.1 m^-1(Vy)²           dVy/dt = - 0.1 s^-2(X)

determine (estimate) X, Y, Vx, and Vy at time 0.01s.

• To determine whether a given function of time is the correct solution of given equations of motion with a specified initial position and velocity, or to use initial conditions to decide which of a family of possible solutions is the correct one.

• To find the future positions and/or velocities of an object given the initial position and velocity when the forces are constant or specific functions of time.

32) A race car's engine exerts a force F(t) = (10000 N/s³) t³. If the car is travelling at velocity 20m/s at time t=1s, how fast is the car moving at t=3s? How far does the car travel between 1s and 3s?