An object moves in a circular orbit starting from rest. the orbit has a radius of 10 m. it takes 10 revolutions to reach its final speed of 10 m/s. a) how far did it travel from rest to its final speed (in meters)?
b) if it accelerated at a constant rate, what was its tangential accelerate during that time?
c) once it reaches its final speed, what is its centripetal acceleration?
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Ответ:
a)![d=628.3m](/tpl/images/0305/0145/cbea4.png)
b)![a_t=5m/s^2](/tpl/images/0305/0145/b0cd6.png)
c)![a_{cp}=10m/s^2](/tpl/images/0305/0145/ea693.png)
Explanation:
a) If it did 10 revolutions, it returned to the original point, but it travelled 10 times the circunference
, where r is the radius of the circle, so we have ![d=10(2\pi r)=20\pi (10m)=628.3m](/tpl/images/0305/0145/b9561.png)
b) The tangential component of this problem can be treated as a one dimensional problem, so the (tangential) acceleration
needed to reach the final speed given starting from rest after traveling a distance d can be obtained using the equation for accelerated motion
, so we have:
c) We use our values in the formula for centripetal acceleration given the tangential velocity and radius:
Ответ:
the use of external objects