when a 50N object is hung from the 20cm mark of a 100cm uniform metal tube which is pivoted at 40cm mark,the tube balances.calculate the weight of the tube
cg is at 50 cm mark. measuring torque from 40cm mark.
counterclosetorque+clockwisetorque=0
10cm*Weight+(-20cm*50N)=0
weight= 100N
To calculate the weight of the tube, we need to consider the principle of torque. Torque is the measure of how effectively a force can rotate an object. It is calculated by multiplying the force applied by the perpendicular distance between the axis of rotation and the line of action of the force.
In this scenario, the tube is balanced, which means the sum of the torques on each side of the pivot point is zero. The torque due to the weight of the object must be balanced by the torque due to the weight of the tube.
First, let's determine the torque due to the weight of the 50N object hanging from the 20cm mark. Torque is given by the formula:
Torque = Force * Distance
The distance in this case is the perpendicular distance of the 20cm mark from the pivot point, which is 40cm - 20cm = 20cm. Thus, the torque due to the 50N object is:
Torque1 = 50N * 20cm = 1000 Ncm
To balance the tube, an equal and opposite torque must be exerted by the weight of the tube. Let's denote the weight of the tube as Wtubes and the perpendicular distance of the center of mass of the tube from the pivot point as Dtubes.
Using the condition of balance, we get:
Torque1 = Torque2
1000 Ncm = Wtubes * Dtubes
Since the tube is uniform, we can consider its weight as acting at its center of mass, which is located at the 50cm mark. The perpendicular distance, Dtubes, is the distance between the 50cm mark and the 40cm mark, which is 10cm.
Plugging in the values, we have:
1000 Ncm = Wtubes * 10cm
To cancel out the units of centimeters, we need to convert Ncm to Nm. Since 1 Ncm = 0.01 Nm, we have:
10 Nm = Wtubes * 10cm
Dividing both sides by 10cm:
Wtubes = 10 Nm / 10cm
Wtubes = 1 N
Therefore, the weight of the tube is 1 Newton (N).