Please help me with this combined question set. I only got a few parts wrong in

Question

Please help me with this combined question set. I only got a few parts wrong in each so please help me find a solution for the wrong parts (marked with an x) and show me how to get the correct answer.

A person carries plank of wood 1 .8 m kng with one hand pushing down on it at one end with a force F1 and the other hand halding it up at 45 cm from the end of the plank with force F2. If the plank has a mass c 17 kg and its center of gravity is at the middle orthe plan, what are e magnitudes ofthe rorces F1 and F2? (The d stance or 45 cm is measured from the location or F1. -166.6 F229988X Additional Materials Reading A uniform ladder stands an a rough floor and rests against a frictionless well as shown in the figure Since the flocr is rough, it exerts beth a normal force N and a frictional force fi on the lacder. However, since the wall is frictionless, it exerts only a normal force non the ladder The ladder has a length of L-4.4 m, a weight or W-66.0 N, and rests against the wall a distance d = 3.75 m above the floor. 1f a person with a mass of m-90 kg is standing on the ladder, detenmine the following. (a) the forces exerted on the ladder when the person is halrway up the ladder (Enter the magnitude only-) 1-Draw a careful diagram which includes all forces acting on the ladder. See if you can apply the first condition of equililbrium to vertical forces acting on the ladder in crder to abtain NN N2294.6 -1294.6 (b) the forces exerted on the ledder when the person is three-fourths of the wey up the ladder (Enter the magnitude only.) 258 Draw a careful dlagram which includes all forces acting on the ladder. Make sure your diagram includes the one the force of gravity acting on the person. See if you can apply the first condition of equi brium to vertical forces -change that distinguishes the problem in part(b) from the problem in part (a), namely the point of àpplication of acting on the ladder in order to obtain N1. N N2434.5 4345 Consider the fellowing figure. m= 50.0 kg CG 0.90 m 1.50 m (a) What forca in newtons should the woman in the figure exert on the floor with each hand to do a push-up? Assume that she moves up at a constank speed (b) The triceps muscle at the back of her upper arm has an effective lever arm r 1.77 cm, and she exerts force on the floor at a horizontal distance of 20.8 cm from the elbaw joint. Calculate the magnitude af the force in newtons in each triceps 1727458 | Compare the magnibude af the total force exerted by both triceps muscles to her weight total force exerted by bath triceps muscles her weight = | 3.525 (c) How much work does she do in joules if her center of mass rises 0.275 m? (d) What is her useful power output in watts if she dces 26 push-ups in one minute?

Explanation / Answer

I will do only first two Questions at one time.

1) This is a torque problem. Let the pivot point be at the left end of the plank. This is where F1 pushing down. Let’s determine the weight of the plank.

Weight = 17 * 9.8 = 166.6 N
Counter clockwise torque = 166.6 * 0.9 = 149.94
Clockwise torque = F2 * 0.45
F2 * 0.45 = 149.94
F2 = 149.94 ÷ 0.45= 333.2 N

F1 + 166.6 = 333.2
F1 = 333.2 – 166.6 = 166.6 N

2)

1) (a) If the vertical projection of the 4.4 m ladder is 3.75 m, then the horizontal projection is
d = (4.4² - 3.75²) m = 2.3 m

If we sum the moments about the base of the ladder, we can ignore the friction and normal forces at the floor. The sum of the moments must be zero, or the ladder would be rotating. Then
M = 0 = N2 * 3.75m - ½ * 66N * 2.3m - ½ * 90kg * 9.8m/s² * 2.3m
N2 = 290.7 N

Summing the horizontal forces, observe that f1 = N2 = 290.7 N

Summing the vertical forces, observe that N1 = 66N + 90kg * 9.8m/s² = 948 N

(b) Now M = 0 = N2 * 3.75m - ½ * 66N * 2.3m - (3/4) * 90kg * 9.8m/s² * 2.3m
N2 = 425.96 N
and therefore f1 = 425.96 N
Vertical load unchanged, so N1 = 948 N

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