ExRx.net:
I believe there is some incorrect information presented on your website (see below). Resistance arm and force arm should be defined as the “perpendicular” distance from axis to point of force application. When you are considering forces applied to levers, you are dealing with torques. T= f X perpendicular distance. The physical distance and the perpendicular distance can be the same, or they can be different, depending on whether or not the force is being applied at a right angle (perpendicular) to the lever. Perpendicular distance can be calculated by multiplying the physical distance X the sine of the angle of force application.
In the diagram of the variable resistance machines, the perpendicular distance (shortest distance from line of force to axis) from resistance force to axis does not change. The physical distance from axis to resistant force point of application does change. But the perpendicular distance does not change. Therefore, the resistant torque does not change. However, the effort torque (force X perpendicular distance) does change. The effort torque decreases thus making the movement more difficult. The resistant torque remains constant.
Using the diagram below, simply extend the line of force for the resistance and the force. Then simply draw a line from the axis to the extended line, making sure to create a right angle __I__. You will see that the resistant arm remains the same while the force arm shortens.
Dr. Robert Koslow


Dr. Koslow,
Thank you for your insightful comments. This is what I am considering placing on this page based on your first recommendation:
When calculating forces applied to levers, torque loads must be considered. Torque = Force x Perpendicular Distance. The physical distance and the perpendicular distance are the same only when force is being applied at a right angle (perpendicular) to the lever. Perpendicular distance can be calculated by multiplying the physical distance x sine of the angle of force application.
Now, let me try to understand what you are telling me in the case of the Variable Resistance Lever. In the first figure, forces are perpendicular (90°). In the second figure, both the resistive and motive forces are acting on the lever at approximately 35°, so there are no relative differences between the resistive and motive forces based on that fact alone. However, the physical distance the resistive force increases from the fulcrum is approximately 2 fold requiring greater motive force as the weight is lifted.
Your argument is that, even though the physical distance between the resistive force and fulcrum increase, perpendicular distance is the same. I can certainly see that from drawing vertical lines down the mentioned points as you suggest, so perpendicular distance is the same, therefore, you say the resistive torque remains constant.
I don't believe I had made any erroneous statements in this section, it's just stating 'resistive arm becomes longer' may be a bit misleading with no further explanation and clarification? I understand you are just urging me to add these comments so it is clearer how these forces are interacting. Is that correct?
I see you are the Head of Health Sciences at James Madison University. That's nice you took the time to offer your advice. I appreciate your feedback.
James Griffing, ExRx.net
Hi James:
The error is in the statement “As motive force (F) acts on lever, resistive arm becomes longer requiring progressively greater motive forces throughout movement.”
The resistant arm is longer. But the angle of resistant force has changed, thus keeping the resistant torque consistent throughout the movement. So, why is more force needed if the resistant torque does not change? The answer is that the motive force physical distance has not changed, but the motive force angle of application has changed. The user is no longer applying a force in an efficient manner. But the difference is that the physical distance of the motive force has not changed. If the resistant force = 10 lbs. and the perpendicular distance = 10 inches,
T= 10 X 10= 100 inlbs. This is true for both diagrams. In order to hold the bar in a steady state, the motive torque in diagram #1= T= 10 lbs. X 10 in.= 100inlbs. In diagram 2 the motive torque will be reduced, not because of the lengthening of the resistant physical distance, but because of the shortened perpendicular distance of the motive arm. If we kept the effort force at 10 lbs, our overall motive torque will be decreased due to the shortened perpendicular distance of the effort force. We need to apply more than 10 lbs of force because our motive perpendicular distance has decreased.
So, why is progressively greater motive force needed when the resistant torque has not changed? Because the motive force perpendicular distance has shortened.
Hope this makes sense.
Dr. Koslow
Dr Koslow,
Thank you for this clarification. I will make these changes on our next site update.
James Griffing, ExRx.net