In the nail puller shown in the figure below you exert a force 53.2 cm from the pivot and the nail is 1.50 cm on the other side. What minimum force must you exert to apply a force of 1380 N to the nail to pull the nail up?
To solve this problem, we can use the principle of moments, which states that the sum of the moments acting on an object in equilibrium is equal to zero.
In this case, the moment of force exerted by you, denoted as F1, can be calculated as:
Moment1 = Force1 × Distance1
Where:
Force1 is the force exerted by you
Distance1 is the distance from the pivot to your force (53.2 cm)
Similarly, the moment of force exerted by the nail, denoted as F2, can be calculated as:
Moment2 = Force2 × Distance2
Where:
Force2 is the force exerted by the nail (1380 N)
Distance2 is the distance from the pivot to the nail (1.50 cm)
Since the nail is being pulled up, the force exerted by the nail acts in the opposite direction to the force exerted by you. Therefore, we have:
F1 = -F2
Using the principle of moments, we can equate the two moments and solve for the force exerted by you:
Moment1 = Moment2
Force1 × Distance1 = Force2 × Distance2
Plugging in the given values:
F1 × 53.2 cm = 1380 N × 1.50 cm
Simplifying:
F1 = (1380 N × 1.50 cm) / 53.2 cm
F1 = 38.805 N
Therefore, the minimum force you need to exert is approximately 38.805 N to apply a force of 1380 N to the nail and pull it up.
To solve this problem, we can use the principle of torque. Torque is defined as the product of the force applied and the distance from the pivot point.
The formula for torque is given by:
Torque = Force × Distance
In this case, we want to find the minimum force required to pull the nail up, which means the torque should be equal to or greater than zero. In other words:
Torque = Force × Distance ≥ 0
Let's calculate the torque for both the force you exert and the force applied to the nail:
Torque exerted by you: Torque_1 = Force_1 × Distance_1
Torque applied to the nail: Torque_2 = Force_2 × Distance_2
Given:
Distance_1 = 53.2 cm (distance from pivot)
Distance_2 = 1.50 cm (distance from pivot)
Force_2 = 1380 N (force applied to the nail)
We want to find the minimum Force_1 required, so we substitute the values into the torque equation:
Force_1 × Distance_1 ≥ Force_2 × Distance_2
Now, we rearrange the equation to solve for Force_1:
Force_1 ≥ (Force_2 × Distance_2) / Distance_1
Substituting the given values:
Force_1 ≥ (1380 N × 1.50 cm) / 53.2 cm
Now, we calculate the minimum force you must exert to pull the nail up:
Force_1 ≥ (2070 N · cm) / 53.2 cm
Force_1 ≥ 38.92 N
Therefore, the minimum force you must exert to apply a force of 1380 N to the nail to pull it up is approximately 38.92 N.