Compute the initial upward acceleration of a rocket of mass 1.5 ✕ 104 kg if the initial upward force produced by its engine (the thrust) is 2.7 ✕ 105 N. Do not neglect the weight of the rocket.
Pleas tell me the steps, I've tried getting the acceleration and adding (g) but it doesn't work.
Note: Subtracting (g) doesn't work either.
Thrust - weight = m a
Thrust = m g + m a
a =( Thrust-mg ) / m
a = Thrust/m - g
a = 27/1.5 - 9.81
= 18 - 9.81 = 8.19 m/s^2
To compute the initial upward acceleration of the rocket, we need to consider the forces acting on it. In this case, we have the thrust force produced by the engine and the weight of the rocket.
1. Calculate the weight:
The weight of an object is given by the formula: weight = mass x gravitational acceleration (w = m x g), where the mass is 1.5 ✕ 10^4 kg and the gravitational acceleration (g) is approximately 9.8 m/s^2. So, the weight of the rocket is:
w = (1.5 ✕ 10^4 kg) x (9.8 m/s^2).
2. Calculate the net force:
The net force acting on the rocket is the difference between the upward force (thrust) and the downward force (weight). Since the weight acts downward, we need to subtract it from the upward thrust:
net force = thrust - weight.
3. Calculate the acceleration:
Using Newton's second law (F = ma), we can rearrange the formula to solve for acceleration. So, the equation becomes:
acceleration = net force / mass.
Now, let's execute these steps and find the initial upward acceleration of the rocket.
1. Calculate the weight:
w = (1.5 ✕ 10^4 kg) x (9.8 m/s^2).
= 1.47 ✕ 10^5 N.
2. Calculate the net force:
net force = thrust - weight.
= 2.7 ✕ 10^5 N - 1.47 ✕ 10^5 N.
= 1.23 ✕ 10^5 N.
3. Calculate the acceleration:
acceleration = net force / mass.
= (1.23 ✕ 10^5 N) / (1.5 ✕ 10^4 kg).
≈ 8.2 m/s^2.
Therefore, the initial upward acceleration of the rocket is approximately 8.2 m/s^2.