A crowbar is used to wrench open a wooden crate. The crowbar is situated so that a point 4 cm from the end digging into the box acts as a pivot point. The crobar is gripped on the other side, 35 cm away from the pivot. If the person exerts a force of 114 lbs on the crobar, how much force is exerted by the crowbar on the box? [Answer in lbs]

To solve this problem, we can use the principle of moments, which states that the moment of a force about a pivot point is equal to the force multiplied by the perpendicular distance from the pivot to the line of action of the force.

In this case, the person is exerting a force of 114 lbs, and the pivot point is located 4 cm from one end of the crowbar. The person grips the opposite end of the crowbar, which is 35 cm away from the pivot point.

The moment exerted by the person's force can be calculated as follows:

Moment = Force × Perpendicular Distance

Moment = 114 lbs × 35 cm

Next, we need to determine the force exerted by the crowbar on the box. Since the crowbar is in equilibrium, the sum of the moments on either side of the pivot point must be equal. This means that the moment exerted by the person's force is equal to the moment exerted by the crowbar on the box.

Therefore, the force exerted by the crowbar on the box can be calculated as follows:

Force on Box × 4 cm = 114 lbs × 35 cm

Now, we can rearrange the equation to solve for the force on the box:

Force on Box = (114 lbs × 35 cm) / 4 cm

Finally, we can calculate the force exerted by the crowbar on the box by substituting the values into the equation:

Force on Box = 9985 lbs / 4 cm

Now we need to convert the units 4 cm to inches. Since there are 2.54 cm in an inch, we divide 4 cm by 2.54 to get the equivalent inches:

4 cm / 2.54 = 1.575 inches

Finally, we can substitute this value into the equation to get the answer in lbs:

Force on Box = 9985 lbs / 1.575 inches

Calculating this, the force exerted by the crowbar on the box is approximately 6342 lbs.