A nonuniform, horizontal bar of mass is supported by two massless wires against gravity. The left wiremakes an angle…
The following solution is suggested to handle the subject “A nonuniform, horizontal bar of mass is supported by two massless wires against gravity. The left wiremakes an angle…“. Let’s keep an eye on the content below!
Question “A nonuniform, horizontal bar of mass is supported by two massless wires against gravity. The left wiremakes an angle…”
A nonuniform, horizontal bar of mass is supported
by two massless wires against gravity. The left wiremakes an angle with the
horizontal, and the right wire makes an angle. The bar
has length .
Find the position of the center of mass ofthe
bar, ,measured from
the bar’s left end.
Express the center of mass in termsof ,, and .
Answer
Concepts and Reason
To solve the problem, you will need to understand the center of mass, the rotational, translational, and tension equilibrium forces.
To determine the tension on the left cord, consider the translational equilibrium force of the block. The tension in the rotational equilibrium of the block can be used to determine the tension. To calculate the center mass, you must rewrite the equation of rotational equilibrium.
Fundamentals
The tension of the rope will include both horizontal and vertical components.
The translational equilibrium will see the forces acting horizontally and vertically balanced. To balance the block, the net horizontal force and vertical force will equal zero.
The rotational equilibrium will balance the vertical and horizontal torques. To balance the block, the net torque acting horizontally as well as the net force acting vertically is equal to zero. The force multiplied by the distance perpendicular to which force acts will give the torque.
As shown in Figure 1, the block is hung as follows:
Here
refers to the tension on left rope.
represents the angle made with left rope by horizontal axis.
indicates tension on right rope.
describes the angle made with right rope by horizontal axis.
refers to the mass of block.
shows acceleration due gravity.
The horizontal axis of translational equilibrium for the block is
Adjust the equation
to adjust the tension on the left. The tension on the left is.
The rotational equilibrium for the block is:
represents the center of mass, and @media_tag_13$ the length of each block.
Substitute HTMLmedia_tag_14$ with HTMLmedia_tag_15$ to create a rotational equilibrium in the block. The block’s rotational equilibrium is.
.
To calculate the block’s center of mass, you can rewrite the equation using the center mass. The center mass of the block is.
is the expression for center mass.
Ans:
is the expression for center mass.
Conclusion
Above is the solution for “A nonuniform, horizontal bar of mass is supported by two massless wires against gravity. The left wiremakes an angle…“. We hope that you find a good answer and gain the knowledge about this topic of science.
is supported
