A 70-kg astronaut floating in space in a M = 118 -kg MMU (manned maneuvering uni

Question

A 70-kg astronaut floating in space in a M = 118 -kg MMU (manned maneuvering unit) experiences an acceleration of 3.00×102 m/s2 when he fires one of the MMU's thrusters.

Part A. If the speed of the escaping N2 gas relative to the astronaut is 530 m/s , how much gas is used by the thruster in 5.00 s ?

Part B What is the thrust of the thruster?

Problem 8.78: Rocket failure!

Just as it has reached an upward speed of 6.00 m/s during a vertical launch, a rocket explodes into two pieces. Photographs of the explosion reveal that the lower piece, with a mass one-fourth that of the upper piece, was moving downward at 2.00 m/s the instant after the explosion.

Part A

Find the speed of the upper piece just after the explosion.

Part B

How high does the upper piece go above the point where the explosion occurred?

A railroad hopper car filled with sand is rolling with an initial speed of 17.5 m/s on straight, horizontal tracks. You can ignore frictional forces on the railroad car. The total mass of the car plus sand is85,000 kg. The hopper door is not fully closed so sand leaks out the bottom. After 22.0 minutes, 1.40×104 kg of sand has leaked out.

Part A

Then what is the speed of the railroad car?

Problem 8.78: Rocket failure!

Just as it has reached an upward speed of 6.00 m/s during a vertical launch, a rocket explodes into two pieces. Photographs of the explosion reveal that the lower piece, with a mass one-fourth that of the upper piece, was moving downward at 2.00 m/s the instant after the explosion.

Part A

Find the speed of the upper piece just after the explosion.

Part B

How high does the upper piece go above the point where the explosion occurred?

A railroad hopper car filled with sand is rolling with an initial speed of 17.5 m/s on straight, horizontal tracks. You can ignore frictional forces on the railroad car. The total mass of the car plus sand is85,000 kg. The hopper door is not fully closed so sand leaks out the bottom. After 22.0 minutes, 1.40×104 kg of sand has leaked out.

Part A

Then what is the speed of the railroad car?

Explanation / Answer

First Problem:

The thrust is F = dm/dt * v where dm/dt is the amount of mass being ejected in kg/second. v is the velocity of the ejected material.

The acceleration on the astronaut is a = F/M where F is the thrust and m is the total mass 70kg + 118kg = 188 kg

so a = dm/dt * v / M

I will let you work the numbers and solve for dm/dt which is the amount of gas used per second. Don't forget that you want the number for 5 seconds and I am assuming that the mass of the gas used is negligible compared to the total mass.

Second Problem:

This problem is the same as doing elastic and inelastic collisions.
So both masses are initially together then separate: (M+M/4)(6.00 m/s)=(M/4)(-2.00)+MV_2
the velocity for M/4 is negative because it is going in the negative direction!
Solve for V_2
For the height, set Kinetic Energy equal to Potential Energy and solve for h. you will know your velocity after you figure out V_2

Hope this helps! :)

Third Problem:

Its simple. The question is sort of a trick question as it tells you to ignore frictional forces.

If no force is acting against the railroad hopper it will neither accelerate or decellerate.

This explains why it starts with an initial velocity of 17.5 ms^-1 and still has a velocity of 17.5 ms^-1 after losing so much weight.

Hope this helped.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.