Question

A student athlete is participating in the hammer throw. The student rotates in uniform circular motion with the mass rotating 2.3 m away from the center of rotation. Refer to the information and diagram above. The University Interscholastic League (UIL) is considering adding an event that increases the length of the chain, doubling the distance from the athlete to the mass. By what factor will the acceleration of the ball change if the speed remains unchanged?

Answer 1

This question involves the concepts of centripetal acceleration and radius of the circlular path.

The acceleration of the ball will change by a factor of "0.5".

The centripetal acceleration of the ball is given by the following formula:

$a_c=\frac{v^2}{r}-------------- eqn(1)$

where,

v = speed  

r = distance of mass from center = radius of circular path = 4 m/s²  

$a_c$ = centripetal acceleration

Therefore, when the radius of the circular path is doubled, the centripetal acceleration becomes:

$a_c'=\frac{v^2}{2r}\\\\a_c'=0.5\frac{v^2}{r}\\\\using\ eqn\ (1):\\\\a_c'=0.5\ a_c$

Learn more about the centripetal acceleration here:

brainly.com/question/14465119?referrer=searchResults

The attached picture explains the concept of centripetal acceleration.