Assignment:
1) A moving electron particle has kinetic energy K. After a net amount of work W has been done on it, the electron is moving one-quarter as fast in the opposite direction. Find W in terms of K. Does your answer depend on the final direction of the electron's motion?
i. This is tricky because surely going from a velocity of v to -¼v should be the same as going from v + ¼v to zero. Is it?
ii. Is going from v to -¼v the same as going from v to ¼v? The starting and finishing kinetic energies are the same, but why would the work required to change be different?
2) A pick-up truck is coasting at a speed vA along a straight and level road. When a load equivalent to 10% of the truck's mass is thrown off the bed, parallel to the ground and in the forward direction, the truck is brought to a halt. If the direction in which this mass is thrown is exactly reversed, but the speed of this mass relative to the truck remains the same, the wagon accelerates to a new speed vB. Calculate the ratio vB/vA.
i. This problem has some deliberate wording. "coasting" implies that the engine is not providing force, and "straight and level road" implies that we can ignore external forces such as gravity. Therefore, all we have to worry about is momentum conservation. Balance the momentum when the truck is moving with the load in its bed to when the truck has come to a stop and the load is thrown forward. What is
the velocity of this load, relative to the trucks initial velocity?
ii. Now solve for when the load is thrown backwards, propelling the truck further forwards. Balance the momentum before and after the mass is thrown and find the new velocity of the truck. The mass of the truck should cancel and you should be able to solve for the ratio vB/vA.
3) A kid on a sled, with a combined mass of 35 kg, is pulled up a slope at constant speed by a tow rope that is parallel to the ground. The ground slopes upwards at a constant angle of 26o above the horizontal and the friction between the sled and the ground is characterized by the coefficient of kinetic friction, μk. Draw a clearly labeled free-body diagram for the kid on a sled. Calculate the tension in the tow rope.
i. The question asks you to draw a FBD - which is good as this is exactly where you should start to solve this problem! What are the forces acting on the sled?
ii. The question states that the kid on the sled are pulled "at constant speed" which means the acceleration and net force are both zero. Recall, that for problems with slopes you resolve the forces parallel and perpendicular to the slope (usually the force that needs splitting up is the weight, mg). All the forces (which recall are vectors) when added together equals zero. In other words, forces up the hill are equal to forces down the hill, and forces in to the hill and equal to forces out of the hill. This being the case, find the tension in the rope.
4) Your driving your car at 15.6 m s-1 (about 35 mph) and the traffic light ahead turns amber. Do you brake before the intersection or hit the gas pedal and beat the light? The light has a speed camera which will automatically deposit a hefty fine in the mail (along with a picture of your car speeding through the intersection or stopping within the intersection) if you get it wrong.
The traffic light will remain amber for 3.5 seconds (Texas state minimum), your reaction time is 0.75 s and the intersection is 10 m wide. When you first saw the light turn amber, you where 40 m in front of the intersection. Your car can accelerate at a rate of 4 m s-2 or decelerate at a rate of 6 m s-2 (taking the coefficient of friction from Homework 2).
In Dallas a speed camera issued 9407 tickets worth $705,525 between January 1 and August 31, 2007. Upon investigation by a local news station it was found that the amber light lasted only 3.15 s. How might the decision of the corrupt local government in Dallas, to put profit before safety and reduce the length of time for the amber light, affect your above predicament?
i. The first part is to consider the car approaching the intersection with a 3.5 s amber light. What would happen if you decided to just continue at the same speed through the intersection? What deceleration would the car require to stop in time? What acceleration would the car require to clear the intersection before the light turns red? Don't forget to include the reaction time in your calculations. Are these values reasonable?
ii. Repeat the same analysis as in part i but with the time that the amber light is on at 3.15 s instead of 3.5 s. How does this change your answers?
5) The chef on the Titanic, Charles Joughin, helped many people onto lifeboats and declined to board one himself. Subsequent to helping others he drank an entire bottle of whiskey, put on a life jacket and, after the Titanic had completely been submerged, stepped onto the bow of the ship without as much as getting his hair wet. Both the alcohol (kept him warm) and the life jacket (kept him afloat) saved his life. His mass was 100 kg and the inflated jacket had a volume of 3.1 x 10-2 cubic meters and was completely submerged under the water. The volume of the chef's body that was underwater is 8.2 x 10-2 cubic meters. What was the density of the life jacket?
This question has a lot of unrequired information, which I think makes it interesting. The relevant part is that the chef was floating in water and kept afloat by the life jacket. A FBD of this situation would see the weight of the chef and life jacket (mass is density multiplied by volume) being equal to the buoyant forces (weight of water displaced). I believe the only unknown (after taking the density of water to be 1000 kg m-3, will be the density of the life jacket.
6) Yikes! Scooby Doo is being chased by the Phantosaur! Scooby Doo very quickly accelerates at 6 ms-2 to his top velocity of 3 m s-1. Scooby Doo, having been chased by lots of ghosts, is good at running and can maintain this velocity. The Phantosaur accelerates at 3 m s-2, and has a top velocity of 6 m s-1. However, the Phantosaur can only maintain such a high velocity for 1 s before getting tired and slowing down at a rate of 1 m s-2. Will the Phantosaur eat Scooby Doo?
This is a tricky intersection problem, because Scooby Doo and the Phantosaur speed up, maintain a constant velocity and (in the case of the Phantosaur) slow down. Therefore, we have to solve this in sections.
i. How long does it take Scooby to accelerate to his top speed and how far has he traveled?
ii. How long does it take the Phantosaur to accelerate to his top speed and how far does it travel? During the time it takes the Phantosaur to get up to its maximum velocity, how far has Scooby ran?
iii. The Phantosaur can only maintain the high velocity for 1 s. After this 1 s, how far has it ran, and how far has Scooby ran?
iv. Finally Scooby maintains a constant velocity, while the Phantosaur slows down. What are the equations for distance traveled by both Scooby and the Phantosaur while the Phantosaur is decelerating?
At any point in the previous steps was the Phantosaur ahead of Scooby Doo?