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Force Problem. Please Help

  1. Sep 19, 2010 #1
    You are in training to be an astronaut. In one of your training simulations, your goal is to land a lunar excursion module (LEM) on the surface of the Moon. This LEM has two rocket engines attached to the center of the craft. The engines typically point at angles of 22.0° in opposite directions from the negative y axis and they generate equal amounts of thrust. This means that as they fire, they provide a combined upward force that does not cause the rocket to move to the right or left.

    In an “accident” intended to test your astronaut skills, the right rocket (labeled B) is bent to a 39.0° angle. The illustration to the right shows these two angles. In spite of this problem, you are still expected to guide the LEM straight down.

    There are two levels in this exercise. In the first, the module is moving downward toward the landing pad as the simulation starts. In this “emergency,” the amount of thrust force from the left engine, labeled A, is jammed at 35,600 N.

    You are allowed to set the amount of force from the right engine. You need to set this amount so there is no net horizontal force. If you set engine B’s force this way, you will land the LEM gently onto the landing pad. Small attitude rockets at the top of the LEM will keep it from rotating, but it will drift left or right if you enter the wrong values.

    To accomplish your first mission, compute the force needed from the right engine and set that value to the nearest 100 N in the simulation.

    The second exercise is harder and is optional. In the second simulation, the LEM is again moving downward toward the landing pad. You need to set the forces of both engines to achieve a net acceleration directly upward of 4.12 m/s2. The mass of the module is 8910 kg, and it does not change significantly as the engines burn fuel. As an astronaut, you know that the rate of acceleration due to the Moon's gravity is 1.62 m/s2.

    To solve this problem, first calculate the total vertical force that should be provided by the engines to counter the Moon's gravity and provide a net upward acceleration of 4.12 m/s2. This will give you one equation involving the two unknown engine forces. The horizontal components of the misaligned engine forces must still balance so that the LEM stays on course. This gives you another equation. Solve the two equations and enter the force values to the nearest 100 N.

    Please help. I do not know where to start. Thanks!
     
  2. jcsd
  3. Sep 20, 2010 #2
    For the first problem:

    Force A Horizontal = 35,600 * sin(22)
    Force B Horizontal = ForceB * sin(39)

    Force B = 35,600*sin(22)/sin(39)

    For the second problem:

    I think you can just add the accelerations to get 5.74m/s^2. Might want to check that part.

    Next calculate the force you'll need F = m*a

    F = 8910 * 5.74
    F = 51143.4

    So your two equations are then:
    Vertical:
    51143.4 = ForceA*cos(22) + ForceB*cos(39)
    Horizontal:
    0 = ForceA*sin(22) + ForceB*cos(39)

    If you can't solve this system of equations, then you are in real trouble. Good luck. :)
     
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