A heavy bank-vault door is opened by the application of a force of 3.0 x 10^2 N directed perpendicular to the plane of the door at a distance of 0.80 m from the hinges. What is the torque?
To find the torque, we need to use the formula:
Torque = Force x Distance x sin(theta)
Where:
- Force is the perpendicular force being applied (given as 3.0 x 10^2 N)
- Distance is the distance from the hinges to the point where the force is applied (given as 0.80 m)
- theta is the angle between the direction of the force and the direction perpendicular to the door (which is 90 degrees since the force is perpendicular)
Now let's calculate the torque using the given values:
Torque = (3.0 x 10^2 N) x (0.80 m) x sin(90 degrees)
First, convert the angle from degrees to radians:
Theta (in radians) = Theta (in degrees) x (π/180)
Theta = 90 degrees x (π/180)
Theta = π/2 radians
Now, substitute the values into the formula:
Torque = (3.0 x 10^2 N) x (0.80 m) x sin(π/2)
Since sin(π/2) equals 1, we can simplify the equation:
Torque = (3.0 x 10^2 N) x (0.80 m) x 1
Finally, multiply the numbers:
Torque = (3.0 x 10^2) x (0.80) Nm
Torque = 240 Nm
Therefore, the torque applied to the bank-vault door is 240 Nm.