crane lifts a 75 kg girder 8.85 m. How much work does the crane do lifting with an upward acceleration of 1.20 m/s ^2?
A=m(g+a)h=75(9.8+1.2)*8.85=7,301.25Joules
To find the work done by the crane in lifting the girder, we need to know the force applied by the crane and the distance over which the force is applied.
The force applied by the crane can be calculated using Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the mass is 75 kg and the upward acceleration is 1.20 m/s^2, so the force applied by the crane is:
F = m * a
= 75 kg * 1.20 m/s^2
= 90 N
Now, we need to calculate the distance over which the force is applied. The distance is given as 8.85 m.
To find the work done, we can use the formula:
Work (W) = Force (F) * Distance (d) * cos(theta)
In this case, since the force and displacement are in the same direction (upward), the angle (theta) between them is 0 degrees, and cos(0) = 1. Thus, we can simplify the formula to:
Work (W) = Force (F) * Distance (d)
Substituting the values:
W = 90 N * 8.85 m
= 796.5 J
Therefore, the crane does 796.5 Joules of work in lifting the girder with an upward acceleration of 1.20 m/s^2.