A man pulled a nail our of a board with a crowbar. The nail was 2 in. from the fulcrum of the crowbar, and the effort applied was 36 in. from the fulcrum. If the theoretical effort applied was 10 lb., what was the force of friction between the board and the nail? How far did the hand have to move in order to move the nail one inch?
I do not know where to start.
IT is a lever.
Mechanical ADvantage= 36/2
ForceonNail= MA*10lb
To solve this problem, let's start by understanding the concept of a lever and mechanical advantage.
A lever consists of a rigid beam that rotates around a fixed point called the fulcrum. In this case, the crowbar is acting as a lever, with the fulcrum being where it is being held.
To solve for the force of friction between the board and the nail, we can use the concept of torque. Torque, measured in unit pounds-inches (lb-in), is the product of force and the perpendicular distance from the fulcrum. In this case, the torque can be represented as:
Torque = Force x Distance
We are given that the theoretical effort applied (force) is 10 lb and the distance from the fulcrum is 36 in. The torque is given by:
Torque (effort) = 10 lb x 36 in = 360 lb-in
Now, let's consider the nail's reaction against the crowbar. When the nail is about to be pulled out, it experiences an equal and opposite force of friction to prevent it from sliding out. This force of friction can be calculated using the same formula:
Torque (friction) = Force (friction) x Distance
Given that the distance from the fulcrum is 2 in, we can rearrange the equation to solve for the force of friction:
Force (friction) = Torque (friction) / Distance
= Torque (effort) / Distance
= 360 lb-in / 2 in
= 180 lb
Therefore, the force of friction between the board and the nail is 180 lb.
Now, to find out how far the hand has to move to move the nail one inch, we can use the concept of mechanical advantage. Mechanical advantage is the ratio of the load force (force required to move the nail) to the effort force applied (force applied by the hand).
Mechanical advantage = Load Force / Effort Force
In this case, the load force required to move the nail one inch is the force of friction between the board and the nail, which we calculated as 180 lb. The effort force is given as 10 lb. Therefore, the mechanical advantage is:
Mechanical advantage = 180 lb / 10 lb
= 18
This means that for every pound of effort applied, the nail will move 18 inches.
To find out how far the hand has to move to move the nail one inch, we can use the formula:
Distance (hand) = Distance (nail) / Mechanical advantage
= 1 in / 18
= 1/18 in
Therefore, the hand would have to move 1/18 inch to move the nail one inch.