A jet of mass 4,768 kg lands on an airstrip, stopping after a distance of 414 m. If the jet has an initial landing speed of 36 m/s, what is the work done, in Joules, by non-conservative forces to stop the jet?
V^2 = Vo^2 + 2a*d. V = 0, Vo = 36 m/s, d = 414 m, a = ?. a will be negative.
F = M*a. W = F*d Joules.
To find the work done by non-conservative forces to stop the jet, we first need to calculate the kinetic energy of the jet before it stops.
The kinetic energy (KE) of an object is given by the formula:
KE = (1/2) * mass * velocity^2
Plugging in the given values:
KE = (1/2) * 4768 kg * (36 m/s)^2
= 0.5 * 4768 kg * 1296 m^2/s^2
= 3107968 J
Now, we know that the work done by non-conservative forces is equal to the change in kinetic energy. In this case, the kinetic energy changes from its initial value to zero since the jet comes to a stop.
Therefore, the work done by non-conservative forces is:
Work = Final KE - Initial KE
= 0 - 3107968 J
= -3107968 J
The work done by non-conservative forces to stop the jet is -3107968 Joules. Note that the negative sign indicates that work is done against the motion of the object, which is the case when an object comes to rest.
To calculate the work done by non-conservative forces, we need to find the net work done on the jet. The net work is equal to the change in kinetic energy of the jet.
The change in kinetic energy is given by the equation:
ΔKE = 1/2 * m * (vf^2 - vi^2),
where ΔKE is the change in kinetic energy, m is the mass of the jet, vf is the final velocity, and vi is the initial velocity.
In this case, the initial velocity, vi, is 36 m/s, and the final velocity, vf, is 0 m/s because the jet comes to a stop.
Plugging in the values, we get:
ΔKE = 1/2 * 4768 kg * (0 m/s - (36 m/s)^2)
Simplifying:
ΔKE = 1/2 * 4768 kg * (-1296 m^2/s^2)
ΔKE = -3119616 J
The negative sign indicates that work is done on the jet by non-conservative forces to bring it to a stop.
Thus, the work done by non-conservative forces to stop the jet is approximately 3,119,616 Joules.