A tapering wooden telegraph pole is 15ft long and its center of gravity is 6ft from one end. It weighs 400lbs. What force is required to lift each end?
To find the force required to lift each end of the wooden telegraph pole, we need to consider the distribution of weight along the length of the pole and its center of gravity.
First, let's understand the weight distribution. Given that the telegraph pole is tapered, we can assume the weight is distributed uniformly along its length, with the center of gravity located at a distance of 6ft from one end. This means that the weight is evenly distributed on the upper and lower halves of the pole.
To calculate the weight per unit length of the pole, we can divide the total weight by the total length:
Weight per unit length = Total weight / Total length
= 400 lbs / 15 ft
Weight per unit length = 26.67 lbs/ft (rounding to two decimal places)
Since the weight is uniformly distributed, the weight below the center of gravity is equal to the weight above the center of gravity. Therefore, each half of the pole weighs half of the total weight, which is:
Weight per half pole = Total weight / 2
= 400 lbs / 2
Weight per half pole = 200 lbs
Now, to calculate the force required to lift each end of the pole, we need to consider the lever arm. The lever arm is the distance between the center of gravity and the end being lifted.
For one end, the lever arm is 6ft, and for the other end, the lever arm is (15ft - 6ft) = 9ft.
The force required to lift each end can be calculated using the principle of moments (torque). The torque is calculated by multiplying the weight per half of the pole by the lever arm:
Force = Weight per half pole × Lever arm
For the end with a 6ft lever arm:
Force = 200 lbs × 6 ft
= 1200 ft-lbs
And for the end with a 9ft lever arm:
Force = 200 lbs × 9 ft
= 1800 ft-lbs
Therefore, the force required to lift each end of the wooden telegraph pole is 1200 ft-lbs for the end with a 6ft lever arm and 1800 ft-lbs for the end with a 9ft lever arm.