Outcome 1

3) When a person raises their heels off the ground, the foot acts like a lever.

(a) Typically we consider the foot as a second class lever, but if we treat the ankle bone as the fulcrum, the tension in the calf muscle as the effort, and the normal force from the floor as the resistance, what class of lever is this system?

(b) Calculate the mechanical advantage of this system.

(c) Calculate the tension applied by the calf muscles () to lift a person with weight of 637 N.

(d)Calculate the force in the ankle joint between the foot and the lower leg bones (). [Hint: Both the normal force from the floor and the calf tension point upward. In order for the foot to be in static equilibrium, the force of the lower leg pushing down on the foot must cancel out both of those upward forces.]

(e) Convert your previous two answers (calf tension and force on ankle) to pounds.

The foot acting as a lever arm. Image Credit: OpenStax College Physics

^[1]

4) The head and neck are also a lever system.

(a) State the class of this lever system.

(b) Calculate the mechanical advantage of this system.

(c)  Calculate the force of tension in the neck muscles () to hold the head in the position shown in the diagram.

(d) Calculate the force on the head-neck joint ().

(e) Convert your previous two answers to pounds.

The head and neck acting as a lever system.Image Credit: OpenStax College Physics

^[2]

5) The structure in the following image remains at rest. What do you know about the force and net torque on the structure?

An inverted triangular structure at rest with a block weighting one side, an arm weighting the other,  and a rocket pushing up on the arm. Rocket images  from http://wpclipart.com are in the Public Domain.

6) An engineer performing an inspection on the structure from the previous exercise and measures 45 m from beneath the center of gravity of the block to the point where the structure contacts the ground. The block weighs 1200 N. She then measures the distance to the beneath the center of gravity of the arm to be 95 m. The arm weighs 1200 N as well. Finally she measures the distance to beneath the rocket to be 150 m from the contact point. She then calculates the force being provided by the rocket.

(a) What value does the engineer get when calculating the force provided by the rocket? [Hint: Pretend the rocket isn’t there and calculate the net torque. Then find the force supplied by the rocket to balance out that net torque.]

(b) The engineer then calculates the normal force on the structure from the ground, what value does she get?

Outcome 3

7) Label the following features in the stress-strain curve of a hypothetical material seen below:

• Toe region
• Elastic region
• Yield point
• Plastic Region
• Ultimate Strength
• Rupture Point
• Failure Region

Data adapted with permission from rubber band stress-strain data originally acquired by Umpqua Community College Students: Brittany Watts, Ashlie DeHart, Hanna Wicks and Juan Martinez.

11) Answer the following questions regarding the material used to create the created the stress-strain graph above.

a) How much force could be applied to a 2 m x 2 m x 10 m long block of this material before reaching the ultimate strength?

b) When operating in the elastic region, how much additional stress would be required to cause an additional  strain of 0.01?

c) What force would cause that amount of stress you found in part b on the 2 m x 2 m block?

d) What actual length would the 10 m long material stretch when put under the strain of 0.01?

e) What is the effective spring constant of this 2 m x 2 m x 10 m long block of this material?