At its natural resting length, a muscle is close to its optimal length for producing force. as the muscle contracts, the maximum force it can deliver decreases. when a muscle is at approximately 80% of its natural length, it cannot contract much more and the force it can produce drops drastically. for a muscle stretched beyond its natural length, the same is true. at about 120% of its natural length, the force that a muscle can exert against drops drastically. this muscle length to force relationship can be demonstrated by doing a chin-up. as you hang from the bar, your biceps muscles are stretched and can produce only a relatively small force. as you get close to the bar, your biceps muscles contract substantially, and you again experience difficulty. the easiest part of the chin-up occurs somewhere in between, when your muscles are close to their natural length.

Amanometer is used to measure the air pressure in a tank. the fluid used has a specific gravity of 1.25, and the differential height between the two arms of the manometer is 34 in. if the local atmospheric pressure is 12.7 psia, determine the absolute pressure in the tank for the cases of the

Calculate the first and second velocities of the car with four washers attached to the pulley, using the formulas v1 = 0.25 m / t1 , and v2 = 0.25 m / (t2 – t1) where t1 and t2 are the average times the car took to reach the 0.25 and the 0.50 meter marks. record these velocities, to two decimal places, in table e.

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?