Respuesta :
Answer:
(a). The magnitude of the total acceleration of the ball is 239.97 m/s².
(b). The angle of the total acceleration relative to the radial direction is 11.0°
Explanation:
Given that,
Radius of the circle = 0.681 m
Angular acceleration = 67.7 rad/s²
Angular speed =18.6 rad/s
We need to calculate the centripetal acceleration of the ball
Using formula of centripetal acceleration
[tex]a_{c}=\omega^2\times r[/tex]
Put the value into the formula
[tex]a_{c}=(18.6)^2\times0.681[/tex]
[tex]a_{c}=235.5\ m/s^2[/tex]
We need to calculate the tangential acceleration of the ball
Using formula of tangential acceleration
[tex]a_{t}=r\alpha[/tex]
Put the value into the formula
[tex]a_{t}=0.681\times67.7[/tex]
[tex]a_{t}=46.104\ m/s^2[/tex]
(a). We need to calculate the magnitude of the total acceleration of the ball
Using formula of total acceleration
[tex]a=\sqrt{a_{c}^2+a_{t}^2}[/tex]
Put the value into the formula
[tex]a=\sqrt{(235.5)^2+(46.104)^2}[/tex]
[tex]a=239.97\ m/s^2[/tex]
(b). We need to calculate the angle of the total acceleration relative to the radial direction
Using formula of the direction
[tex]\theat=\tan^{-1}(\dfrac{a_{t}}{a_{c}})[/tex]
Put the value into the formula
[tex]\theta=\tan^{-1}(\dfrac{46.104}{235.5})[/tex]
[tex]\theta=11.0^{\circ}[/tex]
Hence, (a). The magnitude of the total acceleration of the ball is 239.97 m/s².
(b). The angle of the total acceleration relative to the radial direction is 11.0°
