6. A rocket burning its onboard fuel while moving through space has velocity −→v (t) and mass m(t) at time t. If the exhaust gases escape with velocity −→v e, relative to the rocket, then md−→v /dt = dm/dt−→v e. (a) Show using this equation that −→v (t) = −→v (0) − ln(m(0)/m(t))−→v e; (b) If the rocket accelerates in a straight line from rest to twice the speed of its exhaust gases, then what fraction of its initial mass would the rocket have to burn as fuel?

Look at the potential energy diagram for a chemical reaction. which statement correctly describes the energy changes that occur in the forward reaction?

You are still fascinated by the process of inkjet printing, as described in the opening storyline for this chapter. you convince your father to take you to his manufacturing facility to see the machines that print expiration dates on eggs. you strike up a conversation with the technician operating the machine. he tells you that the ink drops are created using a piezoelectric crystal, acoustic waves, and the plateau-rayleigh instability, which creates uniform drops of mass m = 1.25 ✕ 10−8 g. while you don't understand the fancy words, you do recognize mass! the technician also tells you that the drops are charged to a controllable value of q and then projected vertically downward between parallel deflecting plates at a constant terminal speed of 20.0 m/s. the plates are ℓ = 2.15 cm long and have a uniform electric field of magnitude e = 6.40 ✕ 104 n/c between them. noting your interest in the process, the technician asks you, "if the position on the egg at which the drop is to be deposited requires that its deflection at the bottom end of the plates be 0.17 mm, what is the required charge on the drop (in c)? " you quickly get to work to find the answer. (neglect the force of gravity.)

Diego is trying to lift a piano to the second floor of his house. diego uses a pulley system and gives a big lift to the piano.the piano moves upward, then stops, and then it starts to fall to the ground. which list best describes the forces on the piano in the proper order? positive force → balanced force → negative force negative force → balanced force → positive force positive force → unbalanced force → negative force negative force → unbalanced force → positive force