Ahouse painter uses the chair-and-pulley arrangement of (figure 1) to lift himself up the side of a house. the painter's mass is 55 kg and the chair's mass is 10 kg .

if the painter is at rest, what is the tension in the rope?

Explanation:

Draw a free body diagram for the painter.  There are three forces acting on him.  The tension in the rope pulling him up, the normal force of the chair pushing him up, and gravity pulling him down.

Apply Newton's second law:

∑F = ma

T + N - W = ma

Since the painter is at rest, a = 0.

T + N - W = 0

T = W - N

T = Mg - N

Now draw a free body diagram of the chair.  The chair has three forces acting on it also.  The tension in the rope pulling it up, the normal force pushing down, and gravity pulling down.

Newton's second law for the chair:

∑F = ma

T - W - N = ma

Since the chair is also not accelerating, a = 0:

T - W - N = 0

T = W + N

T = mg + N

Now we have two equations and two variables.  If we add the equations together, we can eliminate N:

2T = Mg + mg

2T = (M + m) g

T = (M + m) g / 2

Given that M = 55 kg, m = 10 kg, and g = 9.8 m/s²:

T = (55 + 10) (9.8) / 2

T = 318.5 N

If we round to two sig-figs, the tension in the rope is 320 N.

i wanna say it’s between b and d, leaning more towards b.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.