"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 5.0 m/s. His mass, including the propulsion unit, has the approximately constant value of 143 kg. Find the work done by the force generated by the propulsion unit.
work= final KE + final PE
= 1/2 m v^2+ mgh
20376.6
To find the work done by the force generated by the propulsion unit, we can use the work-energy theorem.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
Given that Rocket Man starts from rest and reaches a speed of 5.0 m/s, we can find the change in kinetic energy.
The change in kinetic energy (ΔKE) is given by the formula:
ΔKE = 1/2 * m * (vf^2 - vi^2)
where m is the mass of Rocket Man (143 kg), vi is the initial velocity (0 m/s), and vf is the final velocity (5.0 m/s).
Plugging in the values, we get:
ΔKE = 1/2 * 143 kg * (5.0 m/s)^2
ΔKE = 1/2 * 143 kg * 25 m^2/s^2
ΔKE = 1806.25 kg·m^2/s^2
Since work done (W) is equal to the change in kinetic energy (ΔKE), we can conclude that:
W = 1806.25 kg·m^2/s^2
Thus, the work done by the force generated by the propulsion unit is 1806.25 kg·m^2/s^2.
To find the work done by the force generated by the propulsion unit, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done (W) is given by the equation:
W = ΔKE
Where ΔKE is the change in kinetic energy.
Since Rocket Man starts from rest, his initial kinetic energy (KEi) is zero. At a height of 16 m, his final speed (vf) is 5.0 m/s. Therefore, his final kinetic energy (KEf) can be calculated using the equation:
KEf = (1/2) * m * v^2
Where m is the mass of Rocket Man and v is the final velocity.
Substituting the given values:
KEf = (1/2) * 143 kg * (5.0 m/s)^2
Simplifying:
KEf = 1,787.5 J
The change in kinetic energy (ΔKE) is then given by:
ΔKE = KEf - KEi
Since KEi = 0, ΔKE = KEf.
Therefore, ΔKE = 1,787.5 J
So, the work done by the force generated by the propulsion unit is 1,787.5 Joules.