Lab 8: Force and weight ; Density - Measuring force and weight - Determining density - Relating mass, volume and density 1) Copper has a density of about 9.0 g/cm 3. Lead has a density of 11.3 g/cm 3. If you have a cube of lead 2 cm on each edge, and a cube of copper 2 cm on each edge, what would be the ratio of the masses of the 2 cubes? (Note the corrected typo above - you probably figured that out yourself though...) The easy (but long) way to do this problem: Density = mass / volume mass = density volume lead cube: mass = 11.3 g/cm 3 (2 cm 2 cm 2 cm) = 90.4 g copper cube: mass = 9.0 g/cm 3 (2 cm 2 cm 2 cm) = 72.0 g ratio = copper mass / lead copper mass = 72.0 g / 90.4 g = 0.796 (1/0.796 = 1.25 is also an okay answer, for the opposite ratio) The tricky (but short) way to do this problem: Recognize both volumes are equal and equate the volumes: Density = mass / volume volume = mass / density volumecopper = volumelead masscopper / densitycopper = masslead / densitylead masscopper / masslead = densitycopper / densitylead = 9.0/11.3 = 0.796
2) An empty barge with a mass of 20,000 kg measures 20 m 5 m 5 m carries steel scraps. If steel has a density of 8 g/cm 3, what is the maximum volume of steel can the barge hold without sinking? This can be done in steps: a) Find the volume of the barge in m 3. volume = (20 5 5)m 3 = 500 m 3 b) Using the density of water in kg/m 3, find the mass of water the barge could hold. (This is the amount of water the barge displaces.) density = 1000 kg/m 3 (from lab 8) mass = density volume = 1000 kg/m 3 500 m 3 = 500,000 kg c) Subtract the mass of the barge from your answer in b) ; this is the remaining capacity of the barge in kg. 500,000 kg 20,000 kg = 480,000 kg d) Use your mass from c) and the density of steel to solve for the volume of the steel. First, convert the mass to grams to get similar units: mass = 480,000 kg 1000 g/kg = 480,000,000 g volume = mass / density = 480,000,000 g / 8 g/cm 3 = 60,000,000 cm 3 There are 1,000,000 cm 3 in a m 3, so this equals 60 m 3. Lab 9: Uniform Motion - Measuring average speed - Recognizing constant speed on a distance vs. time graph - Finding speed and average speed from a distance vs. time graph
3) A runner runs at a pace of 5 m/sec for 10 minutes, then 7 m/sec for 5 minutes, then slows to 3 m/sec for 15 minutes. What was the runnerʼs average speed for the whole run, in m/sec? average speed = total distance / time total distance is the sum of distances over each segment of time distance = speed time ; also, donʼt forget, minutes have to be converted to seconds: 1st distance = 5 m/sec (10 60) sec = 3000 m 2nd distance = 7 m/sec (5 60) sec = 2100 m 3rd distance = 3 m/sec (15 60) sec = 2700 m total distance = 3000m + 2100m + 2700m = 7800 m total time = (10 + 5 + 15) 60 sec = 1800 sec average speed = 7800 m / 1800 sec = 4.33 m/sec 4) The following plot shows the distance vs. time for a small airplane on a flight.
a) What is the highest speed attained by the airplane on this flight? The highest speed is where the slope is steepest; this is the first line segment. The speed is given by the slope of this line, or the rise over run: speed = (350 0) miles / (2.5 0) hr = 140 miles/hr b) What is the lowest speed attained by the airplane on this flight? The lowest speed is where the slope is the least steep; this is the third line segment, between 5 and 6 hours: speed = (600 550) miles / (6 5) hr = 50 miles/hr c) What is the average speed during the flight? Average speed is TOTAL distance / TOTAL time: average speed = 750 miles / 7.5 hr = 100 miles/hr d) Is this a completely realistic distance vs. time plot for a plane in flight? Why or why not? Not really, because a real plane changing speeds would gradually change speed by accelerating - this plot shows speeds changing instantly, from one constant speed to another, which canʼt really happen. Lab 10: Steering a ball ; Representing motion with graphs - Defining and recognizing inertia - Plotting features on distance vs. time graphs - The Law of Inertia (Newtonʼs 1st Law)
5) The following 4 diagrams show a rolling ball hitting a barrier. In each case, use arrows to trace the path the ball will take, including what direction(s) it will travel when it leaves contact with the barrier: What general rule applies in all 4 of these cases? The law of inertia mandates that the ball continues in a straight line when it is not in contact with a wall (i.e. experiencing a force).
6) Cindy is eating a sandwich on a train moving west at exactly 100 mph at a constant speed. Cindy gets up and walks east at exactly 5 mph at a constant speed with respect to the train car. Little does she know that there is an ant on her sandwich, walking 0.1 mph west at a constant speed with respect to the sandwich. a) Draw a diagram to clarify this confusing situation. b) With what speed and direction does an observer standing on the ground outside the train see Cindy moving? (100 5) mph = 95 mph west c) With what speed and direction does an observer standing on the ground outside the train see the ant moving? (100 5 + 0.1) mph = 95.1 mph west
d) If Cindy suddenly drops the sandwich, what kind of motion will the ant experience, from the perspective of each the ant, Cindy, and an observer standing on the ground outside? The ant will feel itself falling straight down, since there is no acceleration anywhere in the system. Cindy, assuming she keeps walking, will see the ant fall almost straight down, moving with a speed of 0.1 mph toward her as she walks. A person outside the train will see the ant fall, while still moving horizontally at 95.1 mph west.