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?
38.9 N is correct
What is the mechanical advantage of the nail puller?
35.5 is correct
i need the steps to get to those answers
1380 * 1.5 = F * 53.2
so
F = 1380 * 1.5 / 53.2 = 38.9 N
advantage = force out/force in
= 1380/38.9 = 35.5
To determine the minimum force required to apply a force of 1380 N to the nail, and the mechanical advantage of the nail puller, you can use the concept of torque and the lever arm equation.
Step 1: Identify the given information:
- Force applied (F) = 1380 N
- Distance from pivot to force applied (d1) = 53.2 cm
- Distance from pivot to nail (d2) = 1.50 cm
Step 2: Convert the distances to meters:
- Distance from pivot to force applied (d1) = 53.2 cm = 0.532 m
- Distance from pivot to nail (d2) = 1.50 cm = 0.015 m
Step 3: Calculate the torque applied by the person:
- Torque (τ) = Force (F) × Distance (d)
- Torque exerted by the person = F × d1
- Torque exerted = 1380 N × 0.532 m = 733.56 Nm
Step 4: Calculate the torque required to pull up the nail:
- Torque required at the nail (τ2) = F × d2
- Torque required = 1380 N × 0.015 m = 20.7 Nm
Step 5: Calculate the mechanical advantage:
- Mechanical Advantage (MA) = Torque applied / Torque required
- MA = τ / τ2
- MA = 733.56 Nm / 20.7 Nm = 35.5
Step 6: Calculate the minimum force required:
- Minimum force required = F = Torque required / Distance from pivot to nail
- F = τ2 / d2
- F = 20.7 Nm / 0.015 m = 1380 N
So, the minimum force required to apply a force of 1380 N to the nail is 1380 N, and the mechanical advantage of the nail puller is 35.5.
To find the minimum force required to apply a force of 1380 N to the nail using the nail puller shown in the figure, you can use the principle of torque, which states that the torque exerted on an object is equal to the product of the force applied and the distance from the pivot point.
Step 1: Identify the distances:
- The distance at which you exert a force (F1) is given as 53.2 cm.
- The distance from the nail to the pivot (F2) is given as 1.50 cm.
Step 2: Set up the torque equation:
Torque exerted by F1 = Torque exerted by F2
Step 3: Calculate the torques:
Torque exerted by F1 = F1 * d1
Torque exerted by F2 = F2 * d2
Step 4: Equate the torques and solve for F1:
F1 * d1 = F2 * d2
F1 = (F2 * d2) / d1
Substituting the given values:
F1 = (1380 N * 1.50 cm) / 53.2 cm
F1 = 38.9 N
Therefore, the minimum force you need to exert to apply a force of 1380 N to the nail is 38.9 N.
To find the mechanical advantage of the nail puller, you can use the formula:
Mechanical Advantage (MA) = Output Force / Input Force
In this case, the input force is the minimum force you need to exert to pull the nail, which is 38.9 N.
The output force is the force applied to the nail, which is 1380 N.
So, the mechanical advantage is:
MA = 1380 N / 38.9 N
MA ≈ 35.5
Therefore, the mechanical advantage of the nail puller is approximately 35.5.