Final answer:
The mechanical advantage (MA) is 8, and the velocity ratio (VR) is 10, resulting in an efficiency of 80%. To maintain this efficiency with an effort of 50 N, the new length of the inclined plane needed would be 2.5 meters.
Step-by-step explanation:
The question is asking us to calculate the mechanical advantage (MA), velocity ratio (VR), efficiency, and the new length of the inclined plane required to maintain efficiency when using a different effort force. To solve this, we first need to understand the basic principles of machines and work done. In this scenario, the mechanical advantage is the ratio of the load to the effort (MA = Load/Effort), and the velocity ratio is the ratio of the distance moved by effort to the distance moved by load (VR = Distance of Effort/Distance of Load).
The efficiency of a machine is calculated by the formula Efficiency (%) = (MA/VR) × 100. Assuming the friction is negligible, EFF = (Load/Effort)×(VR/VR)× 100. Given that 200 N load is lifted by 25 N effort, the MA would be 200/25 = 8. Since the length of inclined plane is 5m and height is 0.5m, VR would be 5/0.5 = 10. So, the efficiency is (8/10) × 100 = 80%.
For a 50 N effort while keeping the same efficiency constant, we would calculate the new length of the inclined plane. Since efficiency remains constant, and we know the relationship between MA, Load, Effort, and VR, we can derive VR using the new effort: MA = Load / Effort = 200 / 50 = 4. Since MA/VR is constant and we know the original VR (which is 10), the new VR would still need to be 10 to maintain the same efficiency. Therefore, the new length of the plane would be VR × height = 10 × 0.5 = 5 meters. However, since we're given different effort and MA, VR would result differently. We then use the height and the efficiency to calculate the new VR: 0.8 = 4 / VR; VR = 4 / 0.8 = 5. The new length would be VR × height = 5 × 0.5 = 2.5 meters.