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

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts

as a general rule, scissors have blades less than 6 in (15 cm) long and usually have handles with finger holes of the same size. shears have blades scissors used to cut hair or fabric must be much sharper