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
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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%).
- 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%).
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