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nexus9112 [7]
3 years ago
5

In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so

that the ball in her hand moves in a circle. In one instance, the radius of the circle is 0.610 m. At one point on this circle, the ball has an angular acceleration of 67.6 rad/s2 and an angular speed of 17.0 rad/s. (a) Find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) Determine the angle of the total acceleration relative to the radial direction.
Physics
1 answer:
Pepsi [2]3 years ago
4 0

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:

a_r=\omega^2R

Plug in the given values and solve for a_r. This gives,

a_r=(17.0\ rad/s)^2\times (0.610\ m)\\\\a_r=289\times 0.610\ m/s^2\\\\a_r=176.29\ m/s^2

Now, tangential acceleration is given by the formula:

a_t=R\alpha

Plug in the given values and solve for a_t. This gives,

a_t=(0.610\ m)(67.6\ rad/s^2)\\\\a_t=41.236\ m/s^2

Now, the magnitude of total acceleration is given as the square root of the sum of the squares of tangential and centripetal accelerations. Therefore,

a_{Total}=\sqrt{(a_r)^2+(a_t)^2}

Plug in the given values and solve for total acceleration, a_{Total}. This gives,

a_{Total}=\sqrt{(176.29)^2+(41.236)^2}\\\\a_{Total}=181.05\ m/s^2

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:

\theta=\tan^{-1}(\frac{a_t}{a_r})\\\\\theta=\tan^{-1}(\frac{41.236}{176.29})\\\\\theta=13.2\°

Therefore, the total acceleration makes an angle of 13.2° relative to radial direction.

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Explanation:

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How much work is done if 10 N is applied to a 5kg object for 10 meters if there is an opposing force of 5 N
BlackZzzverrR [31]

Answer:

50 J

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An object at rest does not _____ and an object in motion does not _____, unless an _____ force acts upon it
mel-nik [20]

Answer:

An object at rest does not move and an object in motion does not change its velocity, unless an external force acts upon it

Explanation:

This statement is also known as Newton's first law, or law of  inertia.

It states that the state of motion of an object can be changed only if there is an external force (different from zero) acting on it: therefore

- If an object is at rest, it will remain at rest if there is no force acting on it

- If an object is moving, it will continue moving at constant velocity if there is no force acting on it

This phenomenon can be also understood by looking at Newton's second law:

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If the net force is zero, F = 0, the acceleration of the object is also zero, a = 0: therefore, the velocity of the object does not change, and it will continue moving at the same velocity (which can be zero, if the object was at rest).

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A pitcher throws a 0.145-kg baseball at a velocity of 30.0m/s. How
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Answer: 65.25 J

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