The meter stick in the drawing can rotate about an axis located at the 20.0-cm mark. The axis is perpendicular to the screen. A force F acts at the left end; the force is perpendicular to the meter stick and has a magnitude of 175 N. A second force, either F1 or F2, acts at the 80.0-cm mark, as the drawing shows. The meter stick is in equilibrium. Which force, F1 or F2, acts on the meter stick, and what is its magnitude?
F2, magnitude = 71.2 N
71.2N
To determine which force, F1 or F2, acts on the meter stick and its magnitude, we can analyze the given information and use the conditions for rotational equilibrium.
First, let's understand the concept of rotational equilibrium. For an object to be in rotational equilibrium, the sum of the torques acting on it must be zero. Torque is the rotational counterpart of force and is calculated using the formula:
Torque = (Force * Perpendicular distance to the axis of rotation)
In this case, the axis of rotation is located at the 20.0-cm mark, perpendicular to the screen.
To find the force and its magnitude, we can set up an equation using the conditions for rotational equilibrium. Since the meter stick is in equilibrium, both the clockwise and counterclockwise torques acting on it must cancel each other out.
Let's consider the torque produced by the force F acting at the left end. The perpendicular distance between the axis of rotation and the force is 20.0 cm. Therefore, the torque produced by F is:
Torque_F = (175 N) * (20.0 cm)
Now, let's consider the torque produced by either F1 or F2 at the 80.0-cm mark. Let's assume F1, but we'll verify if it satisfies the conditions later. The perpendicular distance between the axis of rotation and F1 is 80.0 cm. Therefore, the torque produced by F1 is:
Torque_F1 = (F1) * (80.0 cm)
Since the meter stick is in equilibrium, the sum of the torques must be zero:
Torque_F - Torque_F1 = 0
Substituting the values we have:
(175 N) * (20.0 cm) - (F1) * (80.0 cm) = 0
Simplifying the equation:
3500 cm·N - 80 cm·F1 = 0
Now, we can solve for F1:
80 cm·F1 = 3500 cm·N
F1 = (3500 cm·N) / (80 cm)
Calculating further:
F1 ≈ 43.75 N
Therefore, the force acting on the meter stick is F1, and its magnitude is approximately 43.75 N.