Imagine a landing craft approaching the surface of the moon of a distant planet. If the engine provides an upward force (thrust) of 2980 N, the craft descends at constant speed; if the engine provides only 2200 N, the craft accelerates downward at 0.46 m/s2.
(a) What is the weight of the landing craft in the vicinity of moon's surface?
N
(b) What is the mass of the craft?
kg
(c) What is the magnitude of the free-fall acceleration near the surface of the moon?
m/s2
In both cases,
thrust=m(g-a)
you are given thrust and a in each case, you have two equations, figure "g", and mass m.
weight=mg of course.
To solve these questions, we will use the concepts of force, weight, mass, and acceleration.
(a) To find the weight of the landing craft, we need to consider that when the craft descends at constant speed, the thrust provided by the engine is equal to the weight of the craft. In this case, the engine provides an upward force of 2980 N. Therefore, the weight of the craft near the surface of the moon is also 2980 N.
(b) The weight of an object can be calculated using the formula:
Weight = mass * acceleration due to gravity
Since we already know the weight of the craft (2980 N) and the acceleration due to gravity is the same near the surface of the moon, we can rearrange the formula to find the mass:
mass = Weight / acceleration due to gravity
Substituting the values, we get:
mass = 2980 N / 9.8 m/s^2 ≈ 304 kg
Therefore, the mass of the craft is approximately 304 kg.
(c) To find the magnitude of the free-fall acceleration near the surface of the moon when the engine provides only 2200 N, we can use Newton's second law of motion:
Force = mass * acceleration
The engine provides a force of 2200 N, and the craft accelerates downward at 0.46 m/s^2. Substituting the values, we get:
2200 N = mass * (-0.46 m/s^2)
Since the acceleration is downward, we use a negative sign. Rearranging the formula, we find:
mass = 2200 N / (-0.46 m/s^2) ≈ -4783 kg
Since mass cannot be negative, this means the downward acceleration cannot be explained solely by the force of the engine. Therefore, there might be some other forces acting on the craft that we are not accounting for.
The magnitude of the free-fall acceleration near the surface of the moon is typically around 1.62 m/s^2.
In summary:
(a) The weight of the landing craft is 2980 N.
(b) The mass of the craft is approximately 304 kg.
(c) The magnitude of the free-fall acceleration near the surface of the moon is typically around 1.62 m/s^2.