Physics 101 Fall 2003 Homework Set 2 Exercises: Chapter 3: 4: Their speeds are the same. However, because they are travelling in different directions, they have different velocities. (Remember that velocity is speed plus direction. Speed tells you how fast you are going but not which direction (like your car's speedometer).) 6: Yes, a car can have a velocity heading north and an acceleration to the south. Let's consider the possibilities: If you are heading north (ie: your velocity is in the northward direction) and accelerating toward the north, then you are increasing your speed without changing direction. If you are heading north and your acceleration is East (or West), then you will change your direction. If you are heading North and your acceleration is South, then you are slowing down. Thus, if you are driving North and you hit the brakes to slow down, your acceleration is Southward. 14: a) Yes, an object can be moving and have zero acceleration. If you are moving at constant speed in a constant direction (ie: at constant velocity), then you have zero acceleration (eg: driving in a straight line at 60 mph). b) Yes, an object can accelerate when its speed is zero. Acceleration tells you what your velocity will be in the future. If I hold a rock, the instant I let go it has zero speed and an acceleration of 10 m/s^2. Similarly, if I get in my car, the instant that I push the gas pedal, I have zero speed and a non-zero acceleration. 26: When I throw a ball straight up, its speed will decrease by 10 m/s every second. Once it reaches its highest point and starts falling back to Earth, its speed will increase by 10 m/s every second. It will take the same time to rise as to fall since it will have exactly the same speed profile (just in reverse). See figure 3.8 on p47. Chapter 4 --------- 6: No, you cannot go around a curver in the absence of a force. If there is no force, then by Newton's second law, you will continue in straight line motion. This is a little less abstract if you consider trying to go around a curve when the road is completely icy. 12: Your empty hand is not hurt by hitting the wall because it does not take much force to stop your hand (it does not have much inertia). If you are holding a heavy load, then it has much more inertia and it takes much more force to stop it. That force hurts. Newton's second law is most applicable (F = ma). As the mass increases, the force needed to make it accelerate (change velocity) also increases. 24: Newton's first law says that constant velocity motion requires no NET force. The force that you apply is not the only force on the wagon. There is also the force of friction from the lawn. (I'm ignoring vertical forces here.) The net force = your force plus the force of friction = 0. There is no contradiction here. 26: If gravity is the only force acting, then your velocity will change by 10 m/s every second (becoming more downward or less upward). a) When the sky diver has reached terminal velocity, he is no longer accelerating. Thus, gravity is not the only force acting on him (there is also air resistance). b) an orbiting satellite feels no air resistance so there is no other force than gravity acting on it. Thus, the satellite is in free fall. Problems: --------- Chapter 3: 4: a) At its highest point, the ball has zero velocity. We discussed this in class. b) one second earlier, it is still travelling upward with a speed of 10 m/s (that way gravity makes it 10 m/s smaller in one second so that it is zero at its highest point). c) 10 m/s down d) One second later its velocity is 10 m/s downward. e) 10 m/s down f) the change in velocity from 1 s before its highest point to 1 s after its highest point is (10 m/s down) minus (10 m/s up) = 20 m/s down. g) 10 m/s^2 downward. 6: The acceleration is the change in velocity divided by the change in time = 30 m/s / 10 s = 3 m/s^2 9: OOPS! I goofed and solved the wrong problem. Here is the correct answer to the correct problem: If there is no air resistance, you can calculate how much time it will take an object to fall 1000 m using the equation d = 1/2 g t^2 or t = sqrt(2d/g) = sqrt(2000 m/10 m/s^2) = sqrt(200 s^2) = 14 s the object's speed will then be v = a * t = 10 m/s^2 * 14 s = 140 m/s (or about 300 mph) Since the problem says 'how fast', I will accept either time or speed as an answer. Estimation: ------------ If you drive 12,000 miles each year, then we need to know your average speed to get the total time you spend in the car. My fastest speed is about 60 mph on the highway. My slowest is about 20 mph. The average is probably around 40 mph (maybe 30, maybe 50, depending on how you drive). That means that I spend 12,000 miles / 40 mph = 300 hours in the car each year. There are almost 3*10^8 Americans so we spend a total of 3*10^8 * 300 hours = 10^11 hours in the car each year. Now we need to convert that to years. There are 24 (hours/day) * 365 (days/year) = about 8000 hours per year. That means that 10^11 hours / 8000 (hours/year) = 10^7 years. That's a lot! At 80 years per life, that's 10^5 or 100,000 lives per year. Note that I rounded off all of my numbers. Since the initial information (what is my average speed) is so inaccurate, it makes no sense to have the other numbers written out to many digits. If you do your math on your calculator, then you should round off your final answer.