Chapter 5, Problem 1DQ

To determine

The tension in the rope and the force the seat exerts on the man.

Answer to Problem 1DQ

The tension in the rope is $T=\frac{mg}{2}$ and the force the seat exerts on the man is $N=\frac{mg}{2}$.

Explanation of Solution

Given Info:

The weight of the man sitting in the chair will be balanced by the tension in the rope.

Thus,

$2T=mg$

• T is the tension in the rope
• m is the mass of the man in the chair
• g is acceleration due to gravity

Re-arrange the expression to find the tension in the rope.

$T=\frac{mg}{2}$ (I)

The expression used for the normal force.

$N=mg-T$ (II)

• N is the normal force exerts on the man

Substitute equation (I) in (II) to find the normal force.

$\begin{array}{c}N=mg-\left(\frac{mg}{2}\right)\\ =\frac{mg}{2}\end{array}$

Conclusion:

The tension in the rope is $T=\frac{mg}{2}$ and the force the seat exerts on the man is $N=\frac{mg}{2}$.