A person exerts a force of 6.0 N at a point which is 90 cm from the hinged side of a door. If the torque is 5.2 N m then determine the angle between the force vector and the line that runs directly from the point to the hinged side.
To determine the angle between the force vector and the line that runs directly from the point to the hinged side, we can use the concept of torque.
Torque is defined as the product of the force applied and the perpendicular distance from the point of application to the axis of rotation. Mathematically, torque (τ) can be calculated using the formula:
τ = F * r * sin(θ),
Where:
τ is the torque,
F is the force applied,
r is the distance from the point of application to the axis of rotation (also known as the lever arm),
θ is the angle between the force vector and the line that runs directly from the point to the hinged side.
In this case, the torque is given as 5.2 N m, and the force applied is 6.0 N. We are required to find the angle θ.
Rearranging the formula, we have:
θ = arcsin(τ / (F * r)),
Now, substitute the given values:
θ = arcsin(5.2 N m / (6.0 N * 0.90 m)).
Evaluating this expression gives the angle θ between the force vector and the line that runs directly from the point to the hinged side.