EK 1001 Mechanical advantage

[GRod18]

Question 444.

A 10 Kg Box accelerates down a frictionless ramp at 5 m/2^2. If the block reaches a velocity of 10m/s at the bottom of the ramp, what is the mechanical advantage to the ramp?

Answer 2:1

EK states that mechanical advantage has to deal with acceleration. How exactly does mechanical advantage contribute to acceleration?

Thanks in advance.

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[549]

Mechanical advantage is d(effort)(resistance), so I think the way you would approach this is to calculate the distance traveled by this box along the ramp (d effort) and compare it to the distance traveled if it were subjected to free-fall (d resistance). If you do this using the kinematics equation:

(vf^2)=(vo^2)+2ad

then you get that the d effort (due to the ramp) is 10m, and the d resistance (due to free-fall) would be 5m. That gives you a d(effort)(resistance) ration of 2:1.

So I guess the way mechanical advantage deals with acceleration is that it's involved in figuring out the distance traveled by the object.

Hope that helps

 

[Rabolisk]

You can even simplify it further. Clearly the work done whether in free-fall or down a ramp is the same. Acceleration due to gravity in free-fall would be 10 m/s^2, whereas the acceleration on the ramp is 5 m/s^2. So the force when the object slides down the ramp is half that when it is in free-fall. Half the force = twice the distance = twice the mechanical advantage.

 

[GRod18]

thanks to both of you!