Newton's Laws of Motion

Question

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 14,400 kg. The thrust of its engines is 33,500 N. (Assume that the gravitational acceleration on the Moon is 1.67 m/s².)

Calculate its magnitude of acceleration in a vertical takeoff from the Moon.

___ m/s²

Could it lift off from Earth? If not, why not?

__No, the thrust of the module's engines is less than its weight on Earth.

__Yes, the thrust of the module's engines is greater than its weight on Earth.

__Yes, the thrust of the module's engines is equal to its weight on Earth.

__No, the thrust of the module's engines is equal to its weight on Earth.

If it could, calculate the magnitude of its acceleration.

__ m/s²

Answer 1

For the first part of the question, we need to consider all of the forces acting on the module. The acceleration of the module is a result of their being a net force. In other words the sum of forces in one direction (for this example, upwards) minus the sum of forces in the opposite direction (for this example downwards). The upwards force here is the thrust and the downward force is that of gravity on the moon. We can then use the following relationships to find the acceleration.

F_gravity = m * g_moon

F_net = F_up - F_down

F_net = m * a

For the second question, we need to consider what are the criteria required for the module to lift off the ground. Notice that a net force (non-zero) being present implies that the module is moving. If there is no thrust, gravity pulls the module down and the ground pushes up just enough so that the module stays in place. When the thrusters are on and the module is trying to lift off, the thrust must overcome gravity. With that in mind, consider how strong is gravity on Earth and therefore how powerful must the thrusters be to lift off? Do the thrusters, as described, satisfy that condition?

Answer 2

F=ma

(don't forget this equation) second law of motion

33500 = 14400 * a

(N is a unit of force, kg is the unit of mass)

solve for a

a = 2.33 m/s^2

now that would be the acceleration in free space, but it's being pulled down by the moon.

Since down is the opposite direction the object is moving it we subtract it from the acceleration

2.33-1.67 = 0.66

so the rocket will move upward at 0.66 m/s

the issue with the rocket on earth is the gravity is instead 9.81 on earth. This is a lot more and if we subtract like before.

2.33-9.81= -7.48

we get a negative number. So it won't go up and if it is in the air it will fall down at 7.48m/s^2.

So it won't I'll let you determine whether it is the first or forth option.