To begin I just need to know how to do thrust.
A lunar lander in powered descent at 100 m above the surface of the moon slows down from a velocity of 20 m/s to 0.5 m/s at constant acceleration. Assume that the lander has a mass of 20,000 kg and that burning the fuel does not change the mass. Answer the following questions.
What is the acceleration of the lander?
We know that the formula for gravitational acceleration due to gravity is g= G X M/R^2
We know G is a constant called universal gravitational constant which is equal to 6.67 x 10^-11 N* m^2/kg^2. M is the mass of the object in which the gravitational acceleration is being found. R is the radius of the object. There is a negative sign in front of the equation because the objects in free fall. The acceleration due to gravity is 1.62 m/s^2 which is about 1/6 that of the acceleration due to gravity on earth.
How long will it take the lander to change velocity from 20 m/s to 0.5 m/s?
Time: V-Vº/a. Time = 20 - .5 / 1.62 ----> 19.5/1.62= 12.04 seconds to change from a velocity of 20 m/s to .5 m/s.
What is the thrust (T) of the engines?
So using the information can you help me find thrust?
a= (v₂²-v₁²)/2h =
=(0.5²-20²)/2•100= - 2 m/s²
F=m(a-g)= 20000•(2-1.62) =2.76•10⁴ N
Sure! To find the thrust (T) of the engines, we first need to determine the net force acting on the lander. We can use Newton's second law, which states that force (F) equals mass (m) multiplied by acceleration (a): F = m * a.
In this case, the force acting on the lander is the thrust generated by the engines, which counteracts the gravitational force pulling the lander towards the moon's surface.
The gravitational force can be calculated using the formula F = m * g, where g is the acceleration due to gravity on the moon (1.62 m/s^2) and m is the mass of the lander (20,000 kg).
Next, we need to find the net force acting on the lander. Since the lander is slowing down at a constant acceleration, the net force is equal to mass multiplied by the deceleration (negative acceleration because it is slowing down).
So, the net force (F_net) is given by F_net = m * (-a), where a is the acceleration.
Setting the gravitational force equal to the net force, we can find the thrust of the engines:
m * g = m * (-a)
Rearranging the equation:
a = -g
Now we substitute the value for acceleration due to the moon's gravity:
a = -1.62 m/s^2
Therefore, the acceleration of the lander is -1.62 m/s^2.
Since acceleration (a) is equal to the change in velocity (Δv) divided by the time it takes (t) to change velocity, we can rearrange the formula to find thrust (T):
T = m * a
Substituting the values:
T = 20,000 kg * (-1.62 m/s^2)
Calculating this, we find that the thrust of the engines is approximately -32,400 Newtons.