In lab, a meter stick has its center of gravity at the 45.5 mark. The stick is supported with a meter stick clamp at the 25.0 mrk. A 3.500 kg mass is hung at the 18.2 cm mark to maintain rotational equilibrium.
Whats is the calculation of the counterclockwise torque provided by the hanging mass?
To calculate the counterclockwise torque provided by the hanging mass, we need to understand the concept of torque and its formula.
Torque, represented by the symbol τ (tau), is a measure of the force's ability to cause rotational motion. It is calculated using the formula:
τ = r * F * sin(θ),
where:
- τ is the torque,
- r is the perpendicular distance from the axis of rotation to the line of action of the force,
- F is the force acting on the object, and
- θ is the angle between the force vector and the line connecting the axis of rotation to the point of application of force.
In this case, the distance from the axis of rotation (center of gravity) to the point of application of force (hanging mass) is the sum of the distances between the center of gravity and the 25.0 cm mark, and between the 25.0 cm mark and the 18.2 cm mark. Therefore:
r = (45.5 - 25.0) cm + (25.0 - 18.2) cm
Next, we need to determine the force acting on the object due to the hanging mass. The force can be calculated using the formula:
F = m * g,
where:
- F is the force,
- m is the mass of the hanging object, and
- g is the acceleration due to gravity (usually taken as 9.8 m/s²).
Plugging in the values, we have:
F = 3.500 kg * 9.8 m/s².
Finally, substitute the values of r and F into the torque formula and calculate the counterclockwise torque provided by the hanging mass.