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?
To find the force Farrowbold holding the ball in position and the tension in the string just before the release, we can use the concept of equilibrium.
Step 1: Resolve forces
The force Farrowbold can be resolved into its vertical and horizontal components:
Farrowbold_y = Farrowbold * sin(θ)
Farrowbold_x = Farrowbold * cos(θ)
Step 2: Determine net force
Since the ball is in equilibrium, the net force acting on it is zero. The net force is the vector sum of the vertical and horizontal forces:
Net force_y = Farrowbold_y - Tension_y
Net force_x = -Tension_x
Step 3: Equate net forces to zero
Since there is no net force acting on the ball in the vertical direction (y-axis):
Net force_y = 0
Farrowbold_y - Tension_y = 0
Tension_y = Farrowbold_y
Similarly, there is no net force acting on the ball in the horizontal direction (x-axis):
Net force_x = 0
-Tension_x = 0
Tension_x = 0
Therefore, the tension in the string just before the release is equal to the horizontal component of Farrowbold:
Tension = Tension_x = 0
Step 4: Calculate the force Farrowbold
The force Farrowbold is equal to the vertical component of the force Tension:
Farrowbold = Farrowbold_y / sin(θ)
Now we can plug in the given values:
Mass of the ball (m) = 2.3 kg
Angle (θ) = 26.4°
First, calculate the vertical component of the force Farrowbold:
Farrowbold_y = Farrowbold * sin(θ)
Next, substitute Tension_y with Farrowbold_y:
Farrowbold_y - Tension_y = 0
Farrowbold_y = Tension_y
Substitute Tension_y with Farrowbold_y in the equation:
Farrowbold = Farrowbold_y / sin(θ)
Farrowbold = Tension_y / sin(θ)
Finally, substitute Farrowbold_y with Farrowbold in the equation:
Farrowbold = Tension_y / sin(θ)
Since Tension_y is equal to Farrowbold_y:
Farrowbold = Farrowbold_y / sin(θ)
The force Farrowbold holding the ball in position is equal to Farrowbold_y itself, which can be calculated using the equation:
Farrowbold = Tension_y / sin(θ) = Farrowbold_y / sin(θ)
Therefore, the force Farrowbold holding the ball in position and the tension in the string just before the release are both equal to Farrowbold_y, which is the vertical component of the force Farrowbold.
Please provide the value of Farrowbold_y or any additional information to calculate the force and tension accurately.