Homework 1 Rocket sled A rocket sled moves along the horizontal plane under the presence of a friction force µmg, where m is the mass of the sled at that moment and µ is the coefficient of kinetic friction. The rocket propels itself by ejecting mass at a constant rate dm/dt = −R (R is a positive number, because the sled’s mass is decreasing with time), and the fuel is ejected at a constant speed u relative to the sled. The sled starts from rest with initial mass M, and stops ejecting fuel when half the mass has been expended. a) How long does it take for the sled to finish ejecting its fuel? b) Write an expression for the mass of the sled as a function of time. c) Using any method you would like, derive the following differential equation governing the motion of the sled: (M − Rt) dv dt = −(M − Rt)gµ + Ru d) Separate variables and integrate to find v(t), the velocity of the sled as a function of time. e) After the rocket stops firing, the sled continues to coast an additional distance d before coming to a stop due to friction. Show that this extra distance is d = u 2 2µg ln(2) − µMg 2Ru 2 f) (Extra credit) Show that the total time of the sled’s journey (including both the propulsion stage and the period of coasting) is independent of the rate R at which the fuel is ejected. Find this time, in terms of u, g and µ. 1

Question 1 what is amperage? is the rate of doing work. is the rate of flow of protons in electric current. represents the amount of pressure behind electron flow. is the rate of flow of electrons in electric current. 2 points question 2 what is voltage? is the rate of doing power. represents the amount of pressure behind electron flow. is the rate of doing work. is the rate of flow of electrons in electric current. 2 points question 3 what is power? is the rate of flow of protons in electric current. is the rate of flow of electrons in electric current. is the rate of doing work. represents the amount of pressure behind electron flow. 2 points question 4 if we multiply volts times amps we get what? power circuit work current 2 points question 5 what are two ways alternating currents are similiar? in both ac and dc electrons flow in the same pattern. in both ac and dc, the flow of electrons changes directions back and forth. both ac and dc are only possible in certain materials with atoms that will allow electron flow. both ac and dc involve the flow of electrons. 4 points question 6 how does the flow of electrons flow in an alternating current? the flow of electrons is always slower in an alternating current than within a direct current. the flow of electrons is not constant and forward; it changes direction back and forth. electrons flow from from a higher affinity to that of a lower affinity. electron flow is constant and only in a forward direction. 2 points question 7 what is the flow like in a direct current? the flow of electrons is not constant and forward; it changes direction back and forth. the flow of electrons is constant and only in a forward direction. the flow of electrons go from a higher affinity to a lower affinity. the flow of electrons are always faster in a direct current. 2 points question 8 how is an electric current able to flow? electrons flow from the higher affinity to lower affinity and electrical current is generated. protons flow from the higher affinity to lower affinity and electrical current is generated. the movement of protons from one atom to another leads to an electric charge. the movement of electrons from one atom to another atom in a line results in a flow of electric current. 2 points question 9 how do electrons move from the two different types of metal in a battery? protons flow from the metal with the lower affinity to the metal with higher affinity and electrical current is generated. electrons flow from the metal with the lower affinity to the metal with higher affinity and electrical current is generated. electrons flow from the metal with the higher affinity to the metal with lower affinity and electrical current is generated. protons flow from the metal with the higher affinity to the metal with lower affinity and electrical current is generated.