a jet engine applies a force of 300 N horizontally to the right against a 50 kg rocket, the force of the air friction 200 N. if the rocket is thrust horizontally 2.0 m, the kinetic energy gained by the rocket is
To find the kinetic energy gained by the rocket, we need to calculate the work done on the rocket.
The work done is given by the equation:
Work = Force x Distance x cos(angle)
In this case, the force applied by the jet engine is 300 N to the right, and the distance moved is 2.0 m horizontally. The angle between the force and the displacement is 0 degrees (cos(0) = 1).
Therefore, the work done on the rocket by the jet engine is:
Work = 300 N x 2.0 m x cos(0) = 600 J
However, there is also a force of air friction opposing the motion, which acts in the opposite direction. The work done by air friction is negative because it is against the direction of motion.
The work done by air friction is given by the equation:
Work = Force x Distance x cos(angle)
In this case, the force of air friction is 200 N, the distance moved is 2.0 m horizontally, and the angle between the force and the displacement is 180 degrees (cos(180) = -1).
Therefore, the work done on the rocket by air friction is:
Work = 200 N x 2.0 m x cos(180) = -400 J
The net work done on the rocket is the sum of the work done by the jet engine and the work done by air friction:
Net Work = Work by jet engine + Work by air friction = 600 J - 400 J = 200 J
The kinetic energy gained by the rocket is equal to the net work done on it:
Kinetic Energy = Net Work = 200 J
Therefore, the kinetic energy gained by the rocket is 200 Joules.
To find the kinetic energy gained by the rocket, we need to calculate the net force acting on the rocket and then use it to determine the work done on the rocket.
Given values:
Force applied by the jet engine (F_applied) = 300 N (horizontally to the right)
Mass of the rocket (m) = 50 kg
Force of air friction (F_friction) = 200 N
Distance traveled by the rocket (d) = 2.0 m
Step 1: Calculate the net force (F_net) acting on the rocket.
F_net = F_applied - F_friction
F_net = 300 N - 200 N
F_net = 100 N
Step 2: Calculate the work done (W) on the rocket using the formula:
W = F_net * d
W = 100 N * 2.0 m
W = 200 J (joules)
Step 3: Calculate the kinetic energy gained (KE) by the rocket using the formula:
KE = ½ * m * v^2, where v is the final velocity of the rocket
Since the rocket starts from rest (initial velocity = 0), the final velocity is given by:
v^2 = (2 * W) / m
v^2 = (2 * 200 J) / 50 kg
v^2 = 8 m^2/s^2
Therefore, the kinetic energy gained by the rocket is:
KE = ½ * m * v^2
KE = ½ * 50 kg * 8 m^2/s^2
KE = 200 J
So, the kinetic energy gained by the rocket is 200 joules.