Respuesta :
Answer:
Mechanical work done to lift the log vertically is 1886.5 J
Explanation:
Consider that the radius of the log is very small compared to the length of the log and its center of mass along horizontal direction is lying to the ground. So, its initial potential energy is zero.
Since the log is uniform, its center of mass coincide with its geometric center.
According to the problem, when the log is vertically lifted, the work done is positive as the direction of force and displacement are same.
Applying Work-Energy theorem,
U₁ + W = U₂
Here U₁ and U₂ are initial and final potential energy of the log and W is the work done on the log to lift it vertically.
Since, U₁ is zero, so the above equation becomes:
W = U₂
The final potential energy, U₂ = (mgl)/2
Here m is mass of the log, l is length of the log and g is acceleration due to gravity.
So,
W = (mgh)/2
Substitute 110 kg for m, 3.5 m for l and 9.8 m/s² for g in the above equation.
[tex]W=\frac{110\times3.5\times9.8}{2}[/tex]
W = 1886.5 J
The mechanical work used to lift a uniform log in the given case is 1886.5 joules.
What is mechanical work?
The amount of energy transferred by a force is termed as mechanical work. It is a scalar quantity like energy, and its unit is joules. One of the example of mechanical work is pushing a table from one end of the room to the other.
Based on the given information:
- The length of the uniform log is 3.5 m.
- The mass of the log is 110 kg.
Now mechanical work can be calculated by using the formula,
Work = mass × gravity × height
Putting the values we get,
Work = 110 × 9.8 × 3.5/2 (In the given case, the height lifted is half of the length)
Work = 1886.5 joules
Thus, the mechanical work in the given case is 1886.5 joules.
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