A worker sits at one end of a 199-N uniform rod that is 2.80 m long. A weight of 120 N is placed at the other end of the rod. The rod is balanced when the pivot is 0.630 m from the worker. Calculate the weight of the worker
To calculate the weight of the worker, we can apply the principle of torque equilibrium. Torque, denoted by the symbol τ, is the product of force and the perpendicular distance between the pivot point and the line of action of the force.
In this case, the total torque exerted by the worker and the weight must be balanced for the rod to remain in equilibrium.
The torque exerted by the worker can be calculated as follows:
τ(worker) = force(worker) × distance(worker pivot)
= weight(worker) × distance(worker pivot)
Similarly, the torque exerted by the weight can be calculated as:
τ(weight) = force(weight) × distance(weight pivot)
= weight(weight) × distance(weight pivot)
Since the rod is balanced, the sum of these torques must be zero:
τ(worker) + τ(weight) = 0
Now, we can substitute the given values into the equation:
weight(worker) × distance(worker pivot) + weight(weight) × distance(weight pivot) = 0
Substituting the given values:
weight(worker) × 0.630 m + 120 N × 2.800 m = 0
Simplifying the equation:
weight(worker) × 0.630 m = -120 N × 2.800 m
Dividing both sides of the equation by 0.630 m:
weight(worker) = (-120 N × 2.800 m)/0.630 m
Calculating the value:
weight(worker) ≈ -536.19 N
The negative sign indicates that the weight of the worker acts in the opposite direction to that of the weight of 120 N. However, since weight is usually considered a positive quantity, the weight of the worker can be approximated as:
weight(worker) ≈ 536.19 N
Therefore, the weight of the worker is approximately 536.19 Newtons.