The diameter of the head of a screw nail is 4cm and it's pitch 0.5cm. If the nail can magnify the applied effort 20times .calculate it's MA, VR and efficiency
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The diameter of the head of a screw nails is 4cm and it's pitch 0.5cm. If the nails can magnify the applied effort 20 times, calculate it's MA, VR and efficiency
The screw nail is a simple machine that uses the principle of the inclined plane to magnify the applied force. Here are the calculations for its MA, VR, and efficiency:
- MA (mechanical advantage) = length of the inclined plane / height of the inclined plane
- The length of the inclined plane is the pitch, which is given as 0.5cm
- The height of the inclined plane is the circumference of the screw, which is 2πr where r is the radius (half the diameter) of the head. Thus, r = 2cm and circumference = 2π(2) = 4π cm
- Therefore, MA = 0.5cm / (4π cm) = 0.0398 or approximately 0.04
- VR (velocity ratio) = distance moved by the effort / distance moved by the load
- In this case, the distance moved by the effort is the pitch, which is again 0.5cm
- The distance moved by the load is the distance the screw advances for each turn, which is equal to the pitch times the sine of the thread angle. Assuming a standard screw thread angle of 30 degrees, we have sin(30) = 0.5/length of screw advance. Solving for the length of screw advance, we get length = 0.5 / sin(30) = 1 cm.
- Therefore, VR = 0.5cm / 1cm = 0.5 or 1:2 (meaning that the effort must move twice as far as the load, but with less force).
- Efficiency = useful work output / total work input
- Assuming that the useful work output is the same as the load lifted by the nail (i.e. the force required to drive the nail into a solid surface), we can calculate it as follows: force x distance = (applied force x MA) x (pitch x thread angle)
- Let's assume a force of 10N applied to the nail. Then, the work done is W = 10N x pitch = 10N x 0.5cm = 5Ncm. This is the total work input.
- The useful work output is force x distance = (force to lift nail x length lifted). Assuming a load of 2kg (20N), we can calculate the length lifted as follows: length = weight x distance / force = 2000g x 9.8m/s^2 x 1cm / 20N = 9.8cm
- Therefore, the useful work output is W = 20N x 9.8cm = 196Ncm
- Hence, efficiency = 196Ncm / 5Ncm = 39.2% or approximately 0.39.
In summary, the screw nail has a relatively low MA (0.04) but a moderate VR (1:2). Its efficiency is also moderate (39.2%).
To calculate the mechanical advantage (MA), velocity ratio (VR), and efficiency of the nail, we need to use the formulas and information given. Here's how you can calculate each value step-by-step:
1. Mechanical Advantage (MA):
The formula for calculating mechanical advantage is given by MA = effort distance / load distance.
The effort distance is the distance over which the effort is applied, which is equal to the circumference of the head of the screw nail. The circumference of a circle is calculated by multiplying its diameter by π (pi).
effort distance = π * diameter = π * 4cm
The load distance is the distance over which the load moves using the same effort applied on the effort distance. In this case, it is the pitch of the screw nail.
load distance = pitch = 0.5cm
MA = (π * 4cm) / 0.5cm
Now, you can substitute the values and calculate the mechanical advantage.
2. Velocity Ratio (VR):
The velocity ratio is calculated by dividing the distance moved by the effort by the distance moved by the load.
In this case, the distance moved by the effort is the circumference of the head of the screw nail (effort distance) and the distance moved by the load is the pitch of the screw nail (load distance).
VR = effort distance / load distance = (π * 4cm) / 0.5cm
Now, substitute the values and calculate the velocity ratio.
3. Efficiency:
Efficiency is given by the formula: Efficiency = (MA/VR) * 100%
Substitute the calculated values for MA and VR into the formula and calculate the efficiency.
Efficiency = (MA/VR) * 100%
Now, you can substitute the values and calculate the efficiency.
By following these steps, you'll be able to calculate the mechanical advantage (MA), velocity ratio (VR), and efficiency of the screw nail.