How Does Hill's Law Affect Lifting Different Weights?

[John3509]

Homework Statement

https://imgur.com/a/OLPyMfK

Homework Equations

F=ma
W=F*d
W=T₂ - T₁

The Attempt at a Solution

For part A i figured it must be E because that is the only one that goes to 0 as the hit says.
but nothing about this problem makes any sense to me.

Where it says "You notice that the smaller the weight you attempt to lift, the quicker you can lift it." , I'm thinking, no, you can lift the higher wights just as fast you need need to apply a larger force.

"However, you also notice that there is a limit to how quickly you can lift even very small weights"
Sure, biologically there is a limit to your strength but theoretically should be able to lift infinitely quick by applying an infinitely large force, on a graph this should show the force going to infinity, each individuals biological limit would be then represented by some maximum point of the Force axis (x axis) which they could reach. And the max "quickness" which they could lift it is the y value corresponding with that point in the F axis. So i would expect the graph to be constantly going up, Larger force, can lift it more quickly.

And why is it representing the quickness which you can lift it as velocity on the y-axis not time?

"The detailed relationship between the contraction velocity of a muscle (the speed with which you can lift something) and the weight you are attempting to lift, is known as Hill’s law."

Especially this makes no sense to me, The velocity is not constant, how can you have a velocity out put for every force input when the force is causing an acceleration?

What is this question supposed to test, the impulse momentum theorem? This question is from a chapter before it is covered, F=ma? W=F*d ? I just can't interpret what is going on here

 

[haruspex]

you can lift the higher wights just as fast you need need to apply a larger force.

The scenario is that you are lifting all weights as fast as you can. If you can summon up a greater force to cope with the larger weights, why weren't you using this greater force with the smaller weights?

biologically there is a limit to your strength

Strength is not the point here. It is a limitation on how fast a muscle can contract.

why is it representing the quickness which you can lift it as velocity on the y-axis not time?

If all lifts are through the same distance, there is a simple connection between time and average velocity. But with the heavier weights you might not manage the full distance, so it's the velocity that matters, not the time.
Further, as noted, power is force times velocity, and there is a limit to the power the muscle can produce. For the most part, the graph illustrates this relationship, i.e. with the same power available, the velocity is inversely proportional to the force. The differences from that are most noticeable at the extremes. As the force required tends to zero (hmm.. that is ignoring the weight of the arm?), the velocity becomes limited by the maximum contraction rate of the muscle; at the other extreme, it becomes limited by the maximum force the muscle can exert.