A crowbar is used to wrench open a wooden crate. The crowbar is situated so that a point 8 cm from the end digging into the box acts as a pivot point. The crobar is gripped on the other side, 29 cm away from the pivot. If the person exerts a force of 110 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 sum of the moments acting on an object must be zero in rotational equilibrium.
In this case, the force exerted by the person is the input or effort force, and the force exerted by the crowbar on the box is the output or resistance force.
The moment of a force is given by the formula: moment = force × distance
Let's calculate the moment of the input force exerted by the person:
moment(input force) = force × distance
moment(input force) = 110 lbs × 29 cm
Next, we need to consider the pivot point, which is where the crowbar is digging into the box. It acts as a fulcrum, and to calculate the moment of the crowbar on the box, we consider the force exerted by the crowbar and its distance from the pivot.
Since we want to find the force exerted by the crowbar on the box, we can use the fact that the sum of moments is zero in rotational equilibrium to find the unknown force.
Moment(input force) + Moment(crowbar on box) = 0
110 lbs × 29 cm + (unknown force) × 8 cm = 0
Now, we can solve this equation for the unknown force:
(unknown force) = -(110 lbs × 29 cm) / 8 cm
Calculating this, we get:
(unknown force) = - 3995 lbs·cm / 8 cm
(unknown force) = - 499.375 lbs
However, it's important to note that the negative sign indicates that the force exerted by the crowbar on the box is in the opposite direction compared to the input force.
So, the magnitude of the force exerted by the crowbar on the box is 499.375 lbs.
Therefore, the force exerted by the crowbar on the box is approximately 499.375 lbs.