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 -1/4 v should be the same as going from v + 1/4v to zero. Is it?
ii. Is going from v to 1/4v the same as going from v to 1/4v? 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, . 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.