Auniform ladder of length l and mass m leans against a frictionless vertical wall, making an angle of 54° with the horizontal. the coefficient of static friction between the ladder and the ground is 0.32. if your mass is four times that of the ladder, what percentage of the way up the ladder can you climb before the ladder begins to slip?

h=0.425 L

Explanation:

Given that

θ =  54°

Coefficient of friction μ = 0.32

Mass of rod = m

Lets take mass of man = M  = 4 m

C is the center of mass of the rod.

By balancing force in y and x direction

R= Fr

R = Fr=  μ N

N = mg + Mg = mg + 4 m g                     ( M =4m)

N = 5 m g

Lets take distance cover by man is h along rod before sliding

Now taking moment about the lower end

M g  h cosθ + m g cosθ L/2  =  R L sinθ

2 M g  h cosθ + m g cosθ L  = 2 R L sinθ

Now by putting the value of R  and M

8 m g  h cosθ + m g cosθ L  = 2  μ N L sinθ

8 m g  h cosθ + m g cosθ L  = 10 m g μ  L sinθ

8   h cosθ +  cosθ L  = 10  μ  L sinθ

8 h + L = 10 μ L tanθ

Now putting the value of θ  and μ

8 h + L = 10 x 0.32 x tan54° x L

8 h + L = 4.4 L

8 h = 3.4 L

h=0.425 L

answer: (431,2)

step-by-step explanation:

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.