A red cart has a mass of 4 kg and a velocity of 5 m/s. There is a 2-kg blue cart that is parked and not moving, thus its velocit
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Answer:
(a) 181.05 m/s²
(b) 13.2°
Explanation:
Given:
Radius of the circle (R) = 0.610 m
Angular acceleration (α) = 67.6 rad/s²
Angular speed (ω) = 17.0 rad/s
(a)
Radial acceleration of the ball is given as:
Plug in the given values and solve for . This gives,
Now, tangential acceleration is given by the formula:
Plug in the given values and solve for . This gives,
Now, the magnitude of total acceleration is given as the square root of the sum of the squares of tangential and centripetal accelerations. Therefore,
Plug in the given values and solve for total acceleration, . This gives,
Therefore, the magnitude of total acceleration is 181.05 m/s².
(b)
Angle of total acceleration relative to radial direction is given by the formula:
Therefore, the total acceleration makes an angle of 13.2° relative to radial direction.