"Rocket Man" has a propulsion unit strapped to his back. He starts from rest on the ground, fires the unit, and accelerates straight upward. At a height of 16 m, his speed is 5.5 m/s. His mass, including the propulsion unit, has the approximately constant value of 139 kg. Find the work done by the force generated by the propulsion unit.
I tried solving for the force upward and got 2126.7N and then applied that to the Work equation (W = force*cos( )*distance) but it keeps saying I'm getting the wrong answer. I tried both 180 and 0 for the angle so I'm not sure what I'm doing wrong.
work done by unit=PE and Ke at16m, 5.5m/s
work done=mg(16)+1/2 m v^2
To find the work done by the force generated by the propulsion unit, you first need to calculate the force upward correctly. Starting from rest, the final speed of 5.5 m/s and the height of 16 m can be used to calculate acceleration using the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity = 5.5 m/s
u = initial velocity = 0 m/s
a = acceleration
s = displacement = 16 m
Substituting the values into the equation:
(5.5 m/s)^2 = (0 m/s)^2 + 2a(16 m)
30.25 m^2/s^2 = 32a
Dividing both sides by 32:
a = 30.25 m^2/s^2 / 32 ≈ 0.9469 m/s^2
Now that we have the acceleration, we can calculate the force using Newton's second law:
F = ma
Where:
m = mass = 139 kg
a = acceleration = 0.9469 m/s^2
Substituting the values:
F = 139 kg * 0.9469 m/s^2 ≈ 131.6291 N
Now that you have the upward force, you can use the formula for work:
Work (W) = force * distance * cos(θ)
Since the rocket is moving vertically upward, the angle θ between the force and displacement is 0 degrees, so cos(θ) = 1.
Substituting the values:
W = 131.6291 N * 16 m * cos(0°)
W = 131.6291 N * 16 m * 1
W ≈ 2106.0656 J (Joules)
Therefore, the work done by the force generated by the propulsion unit is approximately 2106.1 J.