Respuesta :
a) The centripetal acceleration is [tex]1694 m/s^2[/tex]
b) The force on the ball is 321.9 N
c) The direction of the force is upward
Explanation:
a)
The centripetal acceleration of an object in circular motion is given by
[tex]a=\frac{v^2}{r}[/tex]
where
v is the speed of the object
r is the radius of the circle
In this problem, we have:
r = 50 cm = 0.50 m (the radius of the circle is equal to the distance between the shoulder and the ball)
[tex]v=65 mph \cdot \frac{1609 m/mi}{3600 s/h}=29.1 m/s[/tex] is the speed
Substituting,
[tex]a=\frac{29.1^2}{0.50}=1694 m/s^2[/tex]
b)
The force exerted by the hand on the ball is equal to the centripetal force, which is given by:
[tex]F=ma[/tex]
where
m is the mass of the ball
a is the centripetal acceleration
In this problem, we have:
m = 0.19 kg
[tex]a=1694 m/s^2[/tex]
Substituting, we find:
[tex]F=(0.19)(1694)=321.9 N[/tex]
c)
In a uniform circular motion, the direction of the centripetal acceleration is always towards the centre of the circle.
As a result, since the direction of the force is the same as the direction of the acceleration, the direction of the centripetal force is also towards the centre of the circle.
Therefore in this case, since the ball is at the lowest point in the circle, the direction of the force is upward (because it is towards the centre of the circular trajectory).
Learn more about centripetal force and acceleration:
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A) The centripetal acceleration just before the ball leaves her hand is;
α = 1693.6 m/s²
B) The magnitude of the force on her right hand that is exerted on the ball gives; F = 321.8 N
C) The direction of the force her hand exerts on the ball at the point;
Upward direction
We are given;
Mass of ball; m = 0.19 kg
Distance of ball from the pivot at her shoulder; r = 50 cm = 0.5 m
Speed; v = 65 m/h = 29.1 m/s
A) Formula for centripetal acceleration is;
α = v²/r
Thus;
α = 29.1²/0.5
α = 1693.6 m/s²
B) At the lowest point of the circle where the ball has reached maximum speed, magnitude of force which is the centripetal force is gotten from;
F = mv²/r
F = 0.19 * 1693.6
F = 321.8 N
C) Since the ball is now at the lowest point, it means that balls motion will be towards the center and as such the force will be acting in an upward direction.
Read more at; https://brainly.com/question/15089705
