A 60.0 kg rocket accelerates upward from rest reaching a height of 23.4 m in 3.0 seconds. what is the thrust force produced by the engine?
h=at²/2 = > a=2h/t²,
F=ma
To determine the thrust force produced by the rocket's engine, you need to calculate the net force acting on the rocket.
First, let's calculate the acceleration of the rocket using the kinematic equation:
s = ut + 0.5at^2
where s is the distance traveled, u is the initial velocity, t is the time taken, and a is the acceleration.
Given:
Initial velocity, u = 0 (since the rocket starts from rest)
Displacement, s = 23.4 m
Time, t = 3.0 s
Rearranging the equation to solve for acceleration (a):
a = (2s) / t^2
Plugging in the values:
a = (2 * 23.4 m) / (3.0 s)^2
a = 39.0 m/s^2
The acceleration of the rocket is 39.0 m/s^2.
Next, let's calculate the net force acting on the rocket using Newton's second law of motion:
F_net = m * a
where F_net is the net force, m is the mass of the rocket, and a is the acceleration.
Given:
Mass, m = 60.0 kg
Acceleration, a = 39.0 m/s^2
Plugging in the values:
F_net = 60.0 kg * 39.0 m/s^2
F_net = 2340 N
The net force acting on the rocket is 2340 N.
Since the net force acting on the rocket is equal to the thrust force produced by the engine (according to Newton's third law), the thrust force produced by the engine is 2340 N.