Elevator & Rocket Problems

1. A fully loaded Saturn V rocket has a mass of 2.92 x10⁶ kg. Its engines have a thrust of 3.34 x10⁷ N.
   1. What is the force of gravity acting on the rocket at blast-off?
   2. What is the net force acting on the rocket at blast-off?
   3. What is the acceleration of the rocket as it leaves the launch pad?
   4. As the rocket travels upwards, the engine thrust remains constant, but the mass of the rocket decreases. Why?
   5. Does the acceleration of the rocket increase, decrease or remain the same as the engines continue to fire. Justify your answer.

1. Calculate the initial acceleration of a 13,140 kg V-2 rocket bomb fired vertically upwards, if the thrust of its engines is 2.63 x10⁵ N. Calculate the rockets acceleration near "burn-out", when its mass is only 4170 kg. Assume thatthe rockets altitude is low enough that g is still 9.80 N/kg.

1. A 1200 kg rocket is taking off from the surface of the earth. The rocket accelerates up from the Earth at 4.00 m/s². Draw a FBD of the rocket and calculate the thrust of the engines.

1. A passenger in an elevator has a mass of 100 kg. Calculate the force, in Newtons, exerted on the passenger by the elevator if the elevator is:
   1. at rest
   2. moving upwards with an acceleration of 30 cm/s².
   3. moving downwards with an acceleration of 15 cm/s²
   4. moving upwards at a speed of 15 cm/s
   5. free-falling (the cable is broken)

1. An elevator, complete with contents has a mass of 2000 kg. Draw a FBD and calculate the Tension, T, of the elevator cable when:
   1. the elevator is at rest
   2. the elevator moves downwards at 2.0 m/s.
   3. the elevator moves upwards at 2.0 m/s.
   4. moving upwards with an acceleration of 1.0 m/s².
   5. moving downwards with an acceleration of 1.0 m/s²

1. A man measures the acceleration of an elevator by using a spring balance. He fastens the scale to the roof and suspends a mass from it. If the scale reads 98 N when the elevator is at rest and 93 N when it is moving, calculate:
   1. the acceleration of the elevator
   2. the direction the elevator is accelerating in.