Question

pretest: unit 5
a girl with a mass of 22 kg is playing on a swing. there are three main forces acting on her at any time: gravity, force due to centripetal acceleration, and the tension in the swings chain (ignore the effects of air resistance). at the instant shown in the image below, she is at the bottom of the swing and is traveling at a constant speed of 2 m/s. what is the tension in the swings chain at this time? (recall that g = 9.8 m/s²)
a. 237.6 n
b. 97.5 n
c. 180.9 n
d. 117.4 n

Explanation:

Step1: Identify the forces acting

At the bottom of the swing, the net - force equation is $F_{net}=T - mg$, and the net - force provides the centripetal force $F_c$. So $F_{net}=F_c$, and $T - mg=\frac{mv^{2}}{r}$.

Step2: Rearrange the equation for tension

We can solve the equation $T - mg=\frac{mv^{2}}{r}$ for $T$. We get $T = mg+\frac{mv^{2}}{r}$.

Step3: Substitute the given values

Given $m = 22$ kg, $g=9.8$ m/s², $v = 2$ m/s, and $r = 4$ m.
$T=22\times9.8+\frac{22\times2^{2}}{4}$
First, calculate $22\times9.8 = 215.6$ N.
Second, calculate $\frac{22\times2^{2}}{4}=\frac{22\times4}{4}=22$ N.
Then $T=215.6 + 22=237.6$ N.

Answer:

A. 237.6 N