Question

olve for the tension T in the vertical section of string. Express T in terms of the known variables I, m, r, and g

Answer 1

The tension T in the vertical string in equilibrium is equal to the gravitational force acting on the mass m, which is the product of mass m and the acceleration due to gravity g, expressed as T = m × g.

Step-by-step explanation:

To solve for the tension T in the vertical section of the string, we consider the forces acting on the mass at the end of the string in equilibrium. The only forces acting on the mass are the gravitational force (weight) and the tension in the string. The mass experiences a gravitational force (weight) equal to m times g (acceleration due to gravity), which is balanced by the tension in the string since the system is in equilibrium. Therefore, the tension T can be expressed as:

T = m × g

This equation indicates that the tension in the string is directly proportional to the mass of the object hanging from it and the acceleration due to gravity.

Answer 2

The tension T in a vertical string supporting a hanging object of mass m can be calculated using the equation T = mg, where g is the acceleration due to gravity. This equation applies when the string is vertical and the object is motionless.

Step-by-step explanation:

To solve for the tension T in the vertical section of string, we can look at an example where a spider is used to illustrate the principles of tension in a string due to a hanging object. For instance, if a spider of mass m hangs motionless from a vertical strand of its web, the tension T in the string would be equal to the force of gravity acting on the spider. This can be found using the equation T = mg, where g is the acceleration due to gravity. The tension T is the force that the string must exert upward to balance the spider's weight and keep it motionless.

It is important to note that this tension would change if the situation involved angles or if the string was not perfectly vertical. For horizontally oriented strings with angles, or for strings at an incline, the tension needed to maintain equilibrium would also depend on the angles involved, which would require the use of trigonometric functions to resolve the tension components.