To solve the problem of determining the effort needed to lift a load of 150N with a machine that has a velocity ratio of 5 and an efficiency of 75%, we will follow a step-by-step approach. ### Step 1: Understand Key Concepts 1. **Velocity Ratio (VR)**: This is the ratio of the distance moved by the effort to the distance moved by the load. It indicates how many times the effort distance is greater than the load distance. In this case, the VR is given as 5. 2. **Efficiency (η)**: This is a measure of how effectively a machine converts input energy (or effort) into output energy (or work done on the load). It is expressed as a percentage. Here, the efficiency is 75%, or 0.75 in decimal form. 3. **Load (W)**: This is the weight that needs to be lifted, which is given as 150N. 4. **Effort (E)**: This is the force that we need to calculate. ### Step 2: Use the Formula for Efficiency The efficiency of a machine can be expressed with the following formula: \[ \text{Efficiency} (\eta) = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \] Where: - **Mechanical Advantage (MA)** is the ratio of the load lifted to the effort applied. Rearranging the formula gives us: \[ \text{MA} = \eta \times \text{VR} \] ### Step 3: Calculate Mechanical Advantage Substituting the values we have: \[ \text{MA} = 0.75 \times 5 = 3.75 \] ### Step 4: Relate Mechanical Advantage to Load and Effort The Mechanical Advantage can also be expressed as: \[ \text{MA} = \frac{\text{Load (W)}}{\text{Effort (E)}} \] Rearranging this gives us: \[ \text{Effort (E)} = \frac{\text{Load (W)}}{\text{MA}} \] ### Step 5: Substitute the Values Now we can substitute the values we have: \[ E = \frac{150N}{3.75} \] ### Step 6: Perform the Calculation Calculating the effort: \[ E = 40N \] ### Conclusion Thus, the effort needed to lift a load of 150N with the machine is **40N**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A (20N)**: This is incorrect because it suggests a much higher efficiency than what is given. With a VR of 5 and an efficiency of 75%, the effort cannot be this low. - **Option B (30N)**: This is also incorrect. It implies a mechanical advantage that does not align with the given efficiency and VR. - **Option D (50N)**: This option is incorrect as well. It suggests a lower mechanical advantage than what is calculated, which does not satisfy the conditions of the problem. ### Revision Summary - **Velocity Ratio (VR)** indicates how many times the effort distance is greater than the load distance. - **Efficiency (η)** is the ratio of useful work output to total work input, expressed as a percentage. - **Mechanical Advantage (MA)** is calculated using the formula: MA = η × VR. - The effort needed can be calculated using the formula: E = W / MA, where W is the load. This thorough understanding of the concepts and calculations will help in solving similar problems in the future.