Answer :
To find the radius of the loop that the clothes in a dryer travel in, we use the formula for centripetal acceleration:
[tex]\[ a_c = \frac{v^2}{r} \][/tex]
where:
- [tex]\( a_c \)[/tex] is the centripetal acceleration,
- [tex]\( v \)[/tex] is the speed,
- [tex]\( r \)[/tex] is the radius of the loop.
We need to find [tex]\( r \)[/tex], so let's rearrange the formula:
[tex]\[ r = \frac{v^2}{a_c} \][/tex]
We are given:
- The speed [tex]\( v = 35.8 \, \text{m/s} \)[/tex],
- The centripetal acceleration [tex]\( a_c = 3740 \, \text{m/s}^2 \)[/tex].
Now, substitute the given values into the rearranged formula:
[tex]\[ r = \frac{(35.8)^2}{3740} \][/tex]
Calculate the square of the speed:
[tex]\[ (35.8)^2 = 1281.64 \][/tex]
Now, divide by the centripetal acceleration:
[tex]\[ r = \frac{1281.64}{3740} \][/tex]
[tex]\[ r \approx 0.3427 \, \text{m} \][/tex]
So, the radius of the loop is approximately [tex]\( 0.3427 \, \text{meters} \)[/tex].
[tex]\[ a_c = \frac{v^2}{r} \][/tex]
where:
- [tex]\( a_c \)[/tex] is the centripetal acceleration,
- [tex]\( v \)[/tex] is the speed,
- [tex]\( r \)[/tex] is the radius of the loop.
We need to find [tex]\( r \)[/tex], so let's rearrange the formula:
[tex]\[ r = \frac{v^2}{a_c} \][/tex]
We are given:
- The speed [tex]\( v = 35.8 \, \text{m/s} \)[/tex],
- The centripetal acceleration [tex]\( a_c = 3740 \, \text{m/s}^2 \)[/tex].
Now, substitute the given values into the rearranged formula:
[tex]\[ r = \frac{(35.8)^2}{3740} \][/tex]
Calculate the square of the speed:
[tex]\[ (35.8)^2 = 1281.64 \][/tex]
Now, divide by the centripetal acceleration:
[tex]\[ r = \frac{1281.64}{3740} \][/tex]
[tex]\[ r \approx 0.3427 \, \text{m} \][/tex]
So, the radius of the loop is approximately [tex]\( 0.3427 \, \text{meters} \)[/tex].
