A person exerts a force of 28 N on the end of a door 84 cm wide. What is the magnitude of the
torque if the force is exerted
a. perpendicular to the door?
b. at a 45 degree angle to the face of the door?
c. parallel to the door?
a. torque=28(.84)*sin90 Nm
b. torque=28(.84)*sin45 Nm
c. Torque=28*.84*sin0
so it is the product of force times length* sine of angle between force and door.
To calculate the magnitude of the torque in each scenario, we need to use the formula:
Torque = force × distance × sin(θ)
where:
- Torque is the magnitude of the torque
- force is the magnitude of the force applied
- distance is the perpendicular distance from the pivot point (hinge) to the line of action of the force
- θ is the angle between the line of action of the force and a line perpendicular to the door
a. If the force is exerted perpendicular to the door, then the angle θ is 90 degrees. In this case, sin(90°) = 1. Therefore, the formula simplifies to:
Torque = force × distance
Given that the force is 28 N and the door is 84 cm wide, which is equal to 0.84 meters (1 cm = 0.01 m), we can calculate:
Torque = 28 N × 0.84 m = 23.52 N·m
So, the magnitude of the torque when the force is exerted perpendicular to the door is 23.52 N·m.
b. If the force is exerted at a 45-degree angle to the face of the door, then the angle θ is 45 degrees. In this case, we need to use the trigonometric function sin(45°). The formula becomes:
Torque = force × distance × sin(45°)
Since sin(45°) = √2 / 2, the formula simplifies to:
Torque = force × distance × √2 / 2
Applying the values, we have:
Torque = 28 N × 0.84 m × √2 / 2 ≈ 21.27 N·m (rounded to two decimal places)
So, the magnitude of the torque when the force is exerted at a 45-degree angle to the door is approximately 21.27 N·m.
c. If the force is exerted parallel to the door, then there is no perpendicular distance (distance = 0). Therefore, the torque will be zero (0 N·m). Torque is generated when there is a perpendicular distance between the line of action of the force and the pivot point. In this case, since the force and the door are parallel, there is no such distance, resulting in no torque.