08/09/2005 Physics
A crane is lifting a 200 pound object. The crane boom is 50 ft long. The boom forms an 85 degree angle with the horizontal. What is the torque applied to the crane boom?
50 * 200 *cos85 = 872 ft-lb
To find the torque applied to the crane boom, we need to use the formula:
Torque = Perpendicular Force × Distance
Where:
- Perpendicular Force is the component of the force perpendicular to the boom.
- Distance is the distance from the pivot point to the line of action of the force.
First, let's find the perpendicular component of the force. We can do this by multiplying the weight of the object (200 pounds) by the sine of the angle formed by the boom with the horizontal (85 degrees). Remember to convert the weight from pounds to the corresponding unit of force (pound-force) by multiplying it by the acceleration due to gravity (32.2 ft/s²):
Perpendicular Force = 200 pounds × 32.2 ft/s² × sin(85 degrees)
Next, we need to find the distance from the pivot point to the line of action of the force. This distance is the length of the crane boom (50 ft). Hence:
Distance = 50 ft
Now, we can substitute these values into the torque formula:
Torque = Perpendicular Force × Distance
Torque = (200 pounds × 32.2 ft/s² × sin(85 degrees)) × 50 ft
Calculate the value using a scientific calculator or online calculator, and you will get the torque applied to the crane boom.