Two ice-skaters are skating in circles on a frozen pond. Maria is making large circles with a radius of 12 m and skating 4.5 m/s. Her friend, Samantha, is making smaller circles with a radius of 6 m but is not skating as quickly, going only 3.8 m/s. ii. How could each skater increase her centripetal acceleration without changing the size of her path? Explain your reasoning.

v_maria > 4.5 m/s

v_samantha > 3.8 m/s

Explanation:

Formula for centripetal acceleration is;

a_c = v²/r

Where;

v is speed

r is radius

For Maria;

r = 12 m

v = 4.5 m/s

Thus;

a_c = 4.5²/12

a_c = 1.6875 m/s²

For Samantha;

r = 6

v = 3.8 m/s

Thus;

a_c = 3.8²/6

a_c = 2.41 m/s²

We want to find how could each skater increase her centripetal acceleration without changing the size of her path.

From the centripetal acceleration formula, since the size of path can't be changed it means the radius can't be changed and so the only thing that can now increase the centripetal acceleration is when the speed increases.

Thus;

For Maria, she has to move with a faster speed. Thus: v_maria > 4.5 m/s

For Samantha, she also has to move with a faster speed. Thus; v_samantha > 3.8 m/s

it has to be b, about 97 percent.