1. Convert the following x and y vectors to resultant vectors: (4 pts) a. (250 c

Question

1. Convert the following x and y vectors to resultant vectors: (4 pts)

a. (250 cm, 350 cm)

b. (5 m/s, 7 m/s)


2. Convert the resultant vectors into their x and y components. (4 pts)

a. 32.0 m/s at 25 degrees

b. 25.0 N at 70 degrees

Four individuals are having a 4-way tug of war. Each of them is pulling in a different direction.
The amount of force they produce are as follows: (2 pts)

Justin 700 N
Natalie 500 N
Arnold 950 N
Carly 350 N

Assign each of the individuals a direction and then calculate the resultant force vector.



The Gastrocnemius muscle has 2 heads. The pennate fibers in each of the heads pull in different directions. Using the muscle forces and the angles of attachment of each muscle you can calculate the force vectors produced by each of the gastrocnemius heads. Combine the vectors to determine the resultant force acting on the Achilles tendon.

Force produced: Gastrocnemius medialis: 375 N
Gastrocnemius lateralis: 300 N



medial head: 40 degrees, lateral head 45 degrees

Hint: I would draw a separate triangle for each muscle when determining the individual forces.
You need to calculate: the resultant force produced by the two heads of the gastrocnemius on the Achilles tendon (force vectors of GM and GL added up).

Place a textbook on a flat horizontal surface like a desk or tabletop. Then push sideways against the book and feel how much force you can exert before the book begins to move. What force resists the force youexert on the book and prevents the book from sliding

Now place a few more textbooks on top of the first. Again push sideways against the bottom book. Does the force you must exert to start the books sliding change? Explain?

Explanation / Answer

1) a) sqrt(250^2+350^2) = 430.12 cm @ arctan(350/250) = 54.46 degrees b) sqrt(5^2+7^2) = 8.60 m/s @ arctan(7/5) = 54.46 degrees 2) a) x = 32*cos(25) = 29m/s y = 32*sin(25) = 13.5 m/s b) x = 25*cos(70) = 8.55N y = 25*sin(70) = 23.5 N

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