This homework is extra credit!

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1 This homework is extra credit! 1 Translate (10 pts) 1. You are told that speed is defined by the relationship s = d /t, where s represents speed, d represents distance, and t represents time. State this relationship in words, using no mathematical symbols. 2. Impulse is defined as the average force acting on an object multiplied by the time the force acts. If we let J represent impulse, F avg, represent the average force, and t represent the time, is J = Favg /t a correct way of expressing this definition? Explain. 3. The distance that an object travels when it starts from rest and undergoes constant acceleration is one-half the acceleration multiplied by the square of the time. Invent your own symbols and express this statement in symbolic form. Tell me what each symbol represents. 1

2 2 Units (6 pts) Suppose that critters are discovered on Mars who measure distance in boogles and bops. (a) What would the units of speed be in this system? Explain. (b) What would the units of velocity be in this system? Explain. (c) What would the units of acceleration be in this system? Explain. 3 Velocity vs. Time Graph (6 pts) In the graph shown here, velocity is plotted as a function of time for an object traveling in a straight line. (a) Is the velocity constant for any time interval shown? Explain. (b) During which time interval shown does the object have the greatest acceleration? Explain. 2

3 4 Negative Acceleration (4 pts) A car traveling in the forward direction experiences a negative uniform acceleration for 10 seconds. Is the distance covered during the first 5 seconds equal to, greater than, or less than the distance covered during the second 5 seconds? Explain. 5 Graphing (6 pts) A car starts from rest, accelerates uniformly for 5 seconds, travels at constant velocity for 5 seconds, and finally negatively accelerates uniformly for 5 seconds. Sketch graphs of velocity versus time and acceleration versus time for this situation. v (m/s) a (m/s 2 ) t (s) t (s) 3

4 6 Slope and Area (10 pts) The velocity of a car increases with time as shown in the graph below. (a) What is the distance traveled between 0 seconds and 4 seconds? (b) What is the distance traveled between 4 seconds and 8 seconds? (c) What is the total distance traveled by the car? (d) What is the acceleration between 0 seconds and 4 seconds? (e) What is the acceleration between 4 seconds and 8 seconds? 4

5 7 Thrown Ball (6 pts) A ball is thrown downward with a large starting velocity. (a) Will this ball reach the ground sooner than one that is just dropped at the same time from the same height? (b) Will this ball accelerate more rapidly than one that is dropped with no initial velocity? Explain. 8 Gravity (6 pts) A ball is thrown straight upward with positive initial velocity, v i = 2 m/s up, and then returns to the Earth. Let g = 10 m/s 2. (a) Choosing the positive direction to be upward, sketch a graph of the velocity of this ball against time. (b) Where does the velocity change direction? Explain. Indicate this point on your graph. v (m/s) t (s) 5

6 9 Projectiles (10 pts) Two balls are rolled off a tabletop that is 0.8 m above the floor. Ball A has a horizontal velocity of 3 m/s and Ball B has a horizontal velocity of 5 m/s. (a) Assuming g = 10 m/s 2, how long does it take each ball to reach the floor after it rolls off the edge? (b) How far does each ball travel horizontally before hitting the floor? (In other words, what is the range or x f.) (c) If the two balls started rolling at the same time at a point 1.2 m behind the edge of the table, will they reach the floor at the same time? Explain. 10 Newton s 2nd Law (4 pts) The gravitational force acting on a lead ball is much larger than that acting on a wooden ball of the same size and shape. When both are dropped, does the lead ball accelerate at the same rate as the wooden ball? Explain, using Newton s 2nd law of motion. 6

7 11 Elevator (4 pts) If you get into an elevator on the top floor of a large building and the elevator begins to accelerate downward, will the normal force pushing up on your feet be greater than, equal to, or less than the force of gravity pulling downward on you? Explain, using a free-body diagram. 12 Pendulum (8 pts) A pendulum is pulled back from its equilibrium (center) position and then released. (a) What form of energy is added to the system prior to its release? Explain. (b) At what points in the motion of the pendulum after release is its kinetic energy the greatest? Explain. (c) At what points is the potential energy the greatest? Explain. (d) When the pendulum bob is halfway between the high point and the low point in its swing, is the total energy kinetic energy, potential energy, or both? Explain. 7

8 13 Roller Coaster (6 pts) A roller coaster car with a mass of 1350 kg starts at rest from a point 20 m above the ground. At point B, it is 9 m above the ground. (a) What is the initial potential energy of the car? (b) What is the potential energy at point B? (c) If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 40,000 J, what is the kinetic energy of the car at point B? (Hint: Use E i W external = E f, where W external is the work done by external forces, like fricition.) 14 Air Bag Rapid Inflation (4 pts) If an air bag inflates too rapidly and firmly during a collision, it can sometimes do more harm than good in low-velocity collisions. Explain using impulse and momentum ideas why this is the case. 8

9 15 Skateboarder (4 pts) A skateboarder jumps on a moving skateboard from the side. Does the skateboard slow down or speed up in this process? Explain, using conservation of momentum. 16 Bouncing Ball (6 pts) A ball traveling with an initial momentum of 4.0 kg m/s bounces off a wall and comes back in the opposite direction with a momentum of -3.5 kg m/s (assume the negative sign accounts for the ball traveling in the opposite direction). (a) What is the change in momentum of the ball? (b) What impulse is required to produce this change? 9