I need help with this questions.
a). An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 8 feet, and the springs are at their natural length when the door is open. Find the combined lifting force applied to the door by the springs when the door is closed.
Hookes Law:
Forceeachspring=kx
=15/1 * x
and x will be 1/2 *8
f=60
To find the combined lifting force applied to the door by the springs when the door is closed, follow these steps:
1. Determine the distance the springs stretch when the door is closed: Since the springs stretch only one-half the distance the door travels, the distance the springs stretch when the door is closed is given by 8 feet divided by 2, which equals 4 feet.
2. Calculate the force required to stretch each spring when the door is closed: Since a force of 15 pounds is required to stretch each spring 1 foot, the force required to stretch each spring 4 feet is 15 pounds multiplied by 4, which equals 60 pounds.
3. Determine the combined lifting force applied to the door by the springs when the door is closed: Since there are two springs, the combined lifting force applied to the door is the force required to stretch each spring (found in step 2) multiplied by 2. Therefore, the combined lifting force applied to the door by the springs when the door is closed is 60 pounds multiplied by 2, which equals 120 pounds.
So, the combined lifting force applied to the door by the springs when the door is closed is 120 pounds.
To find the combined lifting force applied to the door by the springs when the door is closed, we need to break down the problem into a few steps.
Step 1: Determine the distance the springs stretch when the door is closed.
Since the springs stretch only one-half the distance the door travels, and the door moves 8 feet, the springs will stretch only 8/2 = 4 feet when the door is closed.
Step 2: Calculate the force required to stretch one spring by 4 feet.
Given that a force of 15 pounds is required to stretch each spring 1 foot, we can calculate the force required to stretch one spring by 4 feet. It would be 15 pounds per foot * 4 feet = 60 pounds.
Step 3: Calculate the combined lifting force applied to the door by the two springs.
Since the door has two springs, we need to calculate the combined lifting force.
Therefore, the combined lifting force applied to the door by the two springs would be 60 pounds * 2 = 120 pounds.
So, the combined lifting force applied to the door by the springs when the door is closed is 120 pounds.