Energy when Force is perpendiclar to direction of movement

In summary, the problem is that you need to calculate the energy needed to hold the shuttle static in the x-direction. If you make the shuttle move in a curved path, it will require less energy.
  • #1
jt-walsh
3
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Hello everyone, I made a problem where a shuttle travels to the moon the mine deuterium to fuse on earth, I started incredibly simplistic and I'm working my way up. At first I had the moon static, but now I have the moon moving at a constant radius and constant velocity. I have the shuttle move in a straight line to the moon. Ripping the vectors to calculate the force wasn't to difficult, neither was calculating the energy to over come wind resistance, gravity, to accelerate and jerk in the y direction, but I haven't been able to calculate the energy needed to hold shuttle static in the x-direction.
space ship trig.jpg
Here's a pretty picture I drew to illustrate the problem.

The force due to gravity in the y direction would be the 5.97E24*1E5*G/(6.37E6+Δs)-sin(θ)*7.35E22*G*1E5/z2

The force due to gravity in the x direction would be cos(θ)*7.35E22*1E5*G /z2

z would be the distance between the center of gravity of the moon and the shuttle, 5.97E24 is the mass of the Earth in kg, 7.35E22 is the mass of the moon. The mass of the shuttle would be 100,00 kg

I'm wondering if there's a way to solve for the energy needed if the shuttle travels in a straight line or if I definitely need to make it so that shuttle travels a curved path. (I plan to make it that way later, but right now I'm trying to solve for other things but i want to get this first).

If anyone wants I can give what ψ0 equals, the position equations and other relevant equations.

*edit* apologies, I forgot to factor in the mass of the shuttle and gravitational constant int he force equations.
 
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  • #2
jt-walsh said:
I haven't been able to calculate the energy needed to hold shuttle static in the x-direction.
The only external (to the shuttle) force in the x direction is gravity from the moon. This will get complicated because the moon and shuttle are moving and accelerating and the force is relative to G Mmoon Mshuttle / distance2.

Using a curved path will take much less energy. Once outside the atmosphere, it most efficient to minimize the force used against gravity, so thrust should be perpendicular to gravity (velocity will be an outwards spiral due to the increase in velocity). It's also more efficient to minimize the duration of each thrust impulse.
 
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  • #3
I know using a curved path would be more efficient, but I'm trying to focus on other aspects of the problem, but I can't just leave that part unsolved, and if I changed it I would have to change everything I've already done. However, if it proves too complicated to solve the way I wrote it up I'll have to do that.

Oh, and sorry I forgot to factor in the mass of shuttle and the gravitational constant, I factored them and forgot to put them back in :/
 

FAQ: Energy when Force is perpendiclar to direction of movement

1. What is the relationship between force and energy when the force is perpendicular to the direction of movement?

When the force is perpendicular to the direction of movement, the work done by the force is zero. This means that no energy is transferred to the object in the direction of its movement. However, there may still be a change in the object's potential energy or its rotational energy.

2. What happens to kinetic energy when a force is applied perpendicular to the direction of movement?

Since work done by the force is zero, the object's kinetic energy remains constant. However, if the force causes the object to change direction, its velocity will also change, resulting in a change in its kinetic energy.

3. How does the angle between the force and the direction of movement affect energy?

The angle between the force and the direction of movement determines the amount of work done by the force and, therefore, the amount of energy transferred to the object. When the force is perpendicular to the direction of movement, no work is done and no energy is transferred. As the angle decreases, more work is done and more energy is transferred.

4. Can energy be completely transferred when the force is perpendicular to the direction of movement?

No, energy cannot be completely transferred when the force is perpendicular to the direction of movement. This is because no work is done in the direction of movement, so the object's kinetic energy cannot change. However, there may still be a transfer of potential or rotational energy.

5. How does the principle of conservation of energy apply to a force perpendicular to the direction of movement?

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. This applies to a force perpendicular to the direction of movement because even though no work is done in the direction of movement, there may still be a transfer or transformation of energy in other forms, such as potential or rotational energy.

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