A box weighing 100 newtons is pushed up an inclined plane that is 5 meters long. It takes a force of 75 newtons to push it to the top,which has a height of 3 meters. What is the Mechanical Advantage and Speed Ratio?
To calculate the mechanical advantage and speed ratio in this scenario, we need to understand the definitions of these terms.
1. Mechanical Advantage (MA) is the ratio of the force output by a simple machine to the force input applied to it. It measures how much the machine amplifies the input force.
2. Speed Ratio (SR) is the ratio of the distance the input force moves to the distance the output force moves. It measures how the machine affects the speed of the load.
To find the mechanical advantage:
1. First, we calculate the input force (F1) applied to overcome the weight of the box. In this case, it is given as 75 newtons.
2. Second, we calculate the output force (F2) required to push the box to the top, which is equal to the weight of the box. In this case, it is given as 100 newtons.
3. Finally, we divide the output force (F2) by the input force (F1) to find the mechanical advantage (MA).
MA = F2 / F1
= 100 newtons / 75 newtons
= 4/3 or 1.333
So, the mechanical advantage in this scenario is 1.333 or approximately 4/3.
To find the speed ratio:
1. First, we calculate the distance moved by the input force (d1) along the inclined plane. In this case, it is given as 5 meters.
2. Second, we calculate the distance moved by the output force (d2) vertically to reach the top. In this case, it is given as 3 meters.
3. Finally, we divide the distance moved by the input force (d1) by the distance moved by the output force (d2) to find the speed ratio (SR).
SR = d1 / d2
= 5 meters / 3 meters
= 5/3 or approximately 1.667
So, the speed ratio in this scenario is 1.667 or approximately 5/3.
To summarize:
- Mechanical Advantage (MA) = 4/3 or approximately 1.333
- Speed Ratio (SR) = 5/3 or approximately 1.667