A 250 kg load is lifted 23 m vertically with an acceleration a = 0.185g by a single cable
Determine the tension of the cable.
=2900N
Determine the net work done on the load.
=?
Determine the work done by the cable on the load.
=66700 J
Determine the work done by gravity on the load.
=?
Determine the final speed of the load assuming it started from rest.
=?
Determine the tension of the cable.
=2900N Closer to 2906, but OK
Determine the net work done on the load.
(2900N - 2450)*23 m = 10,350 J
Determine the work done by the cable on the load.
=66700 J OK
Determine the work done by gravity on the load.
-2450*23 = 56,350 J
Determine the final speed of the load assuming it started from rest.
Solve (1/2) M V^2 = 10,350 J for V.
To determine the net work done on the load, we can use the work-energy principle. The work-energy principle states that the net work done on an object is equal to its change in kinetic energy.
The change in kinetic energy (ΔKE) can be calculated as the difference between the final kinetic energy (KEf) and the initial kinetic energy (KEi).
Since the load started from rest, its initial kinetic energy (KEi) is zero. Therefore, we only need to calculate the final kinetic energy (KEf).
The final kinetic energy can be calculated using the equation:
KEf = (1/2) * m * v^2
where m is the mass of the load and v is its final velocity.
In order to find the final velocity, we need to use the kinematic equation:
v^2 = u^2 + 2as
where u is the initial velocity (which is zero since the load started from rest), a is the acceleration, and s is the displacement (23 m in this case).
Substituting the given values, we have:
v^2 = 0 + 2 * 0.185g * 23
Since g is the acceleration due to gravity (approximately 9.8 m/s^2):
v^2 = 2 * 0.185 * 9.8 * 23
Now, we can calculate the final velocity (v) by taking the square root of both sides:
v = √(2 * 0.185 * 9.8 * 23)
After calculating the value of v, you can substitute it into the equation for KEf to find the final kinetic energy of the load.
Finally, the net work done on the load can be calculated as the difference between the final and initial kinetic energy:
Net work = KEf - KEi