Question

1) Short Problems: A. A competitor at a model rocket competition asks your advice - They need to get their rocket to go as high as possible, and they can either use a heavier engine which doubles the velocity it launches with and doubles the mass, or use a lighter engine which will reduce the mass and velocity by 50%. Which should they use, and why? (Assume the rocket expends all its fuel in a very small time interval, and then the rocket is under free fall after that.) B. Imagine swinging a hammer down at a nail in a piece of wood, driving the nail into the wood and bringing the hammer to rest. Is any energy created or transformed in this process? Explain. C. A 550 kg elevator accelerates downwards with a magnitude of ſal = 1.2 m/s for the first 15 m of its motion. How much work is done during this part of its motion by gravity? (Take gravity to be outside the system for this problem.)

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Answer 1

DA) we have assumed the Rocket expends all the fuel in very Short amount of time. So after that the rocket is under free fall. So since gravity is the only force acting on this rocket, energy will be conserved. Our reference point would be assoon as the rocket is expended all fuel and the highest point. As soon as rocket expends all the feel, rocket would have Kinetic energy - į ve and we can regard this as the zero potential surface. So the total energy at this point will be more. Similarly at the highest point , rocket will be at rest and its gravitational potential energy will be mgn. So total energy will be mgh. So since total energy is conserved. Śmu? +0 -0+ mgh * hores agh har So, as we can see, hauz, so more the initial velocity more will be the height. n s Cor destroyed) B) Energy can never be created , it can only be transformed from one form to another. In this case as the collision will not be elastic between hammer and nail. So some energy is lost in the form of heat and friction of nail with the wood. c) mass - 550 kg Gravity will give a - force on the elevator = mg = fg 1 = (550x 9.8).

So, work done by gravity- (S displacement: - 550x 9.8 x 15 = 80850 5