A 2.3 kg ball tied to a string fixed to the ceiling is pulled to one side by a force Farrowbold to an angle of θ = 26.4°.
Just before the ball is released and allowed to swing back and forth, how large is the force Farrowbold that is holding the ball in position?
Just before the ball is released and allowed to swing back and forth, what is the tension in the string?
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To find the force Farrowbold that is holding the ball in position, we can consider the force balance in the vertical direction.
Since the ball is at rest in its initial position, the net force in the vertical direction must be zero. The forces acting in this direction are the weight of the ball, which is given by the equation:
Weight = mass * acceleration due to gravity
Weight = 2.3 kg * 9.8 m/s^2
Weight = 22.54 N
The weight is acting downwards. There is an upward force provided by Farrowbold, and we can find its magnitude by taking the component of Farrowbold in the vertical direction.
The vertical component of Farrowbold can be found by multiplying the magnitude of Farrowbold by the sine of the angle θ:
Vertical component of Farrowbold = Farrowbold * sin(θ)
Plugging in the given values:
Vertical component of Farrowbold = Farrowbold * sin(26.4°)
Now, setting the net force in the vertical direction to zero:
0 = Vertical component of Farrowbold - Weight
0 = Farrowbold * sin(26.4°) - 22.54 N
To solve for Farrowbold, rearrange the equation:
Farrowbold = 22.54 N / sin(26.4°)
Using a calculator, we can find that Farrowbold ≈ 58.35 N.
So, the force Farrowbold required to hold the ball in position is approximately 58.35 N.
Now, let's find the tension in the string just before the ball is released and allowed to swing back and forth.
When the ball is at the lowest point of its swing, the tension in the string is equal to the sum of the weight and the centripetal force required to keep the ball moving in a circular path.
Tension = Weight + Centripetal force
Weight = 22.54 N (from the previous calculations)
The centripetal force can be calculated using the equation:
Centripetal force = mass * velocity^2 / radius
The mass of the ball is 2.3 kg, and the radius is the length of the string. Since nothing is mentioned about the length of the string, we will assume a value. Let's say the length of the string is 2 meters.
Plugging in the values:
Centripetal force = 2.3 kg * velocity^2 / 2 m
Since the ball is at rest just before it is released, the velocity is 0.
Therefore, the centripetal force is 0.
Now, substituting the values in the equation:
Tension = 22.54 N + 0
Tension ≈ 22.54 N
So, the tension in the string just before the ball is released and allowed to swing back and forth is approximately 22.54 N.