If the mass of the ladder is 12.0 kg, the mass of the painter is 55.0 kg, and the ladder begins to slip at its base when her feet are 70% of the way up the length of the ladder, what is the coefficient of static friction between the ladder and the floor

μ = 0.498

Explanation:

I manage to find the picture of this problem. In the attached picture you can also see the forces involved in this case.

We know according to newton's law that the static friction force is:

Fs = μ * N

However, as you can see in the picture, the Normal force is equals to the weight, in this case the weight of the painter and also the ladder, therefore:

N = Fy

and the force of the friction is:

Fs = Fx

Therefore the coefficient is:

μ = Fx/Fy  (1)

Now, let's write the equations in x and y, to solve this.

For the "x" axis:

Fx - Fw = 0 -----> Fx = Fw   (2)

Fw is force of the wall, while Fx is the force friction in the x axis (base of the ladder).

for the "y" axis:

Fy - W1 - W2 = 0

W1 = mg (ladder)

W2 = Mg (painter)

replacing we have:

Fy = W1 + W2

Fy = mg + Mg ----> Fy = g(m + M)    (3)

To get the force that the wall is exerting we need to calculate the torque around the foot of the ladder so:

τ = rF sinθ

However, the angle in the wall and the ladder is 90° so:

τ = rF sin90°

τ = rF   (4)

replacing (4) with the forces we have:

rFw = rW1 + rW2

4Fw = 1.5mg + 2.1Mg

Fw = 1.5mg + 2.1Mg/4   (5)

Finally, with this expression, we can replace it in (1) to get the coefficient of friction:

μ = Fx/Fy

μ = 1.5mg + 2.1Mg / 4g(m + M)     gravity cancels out so:

μ = 1.5m + 2.1M / 4(m + M)

Replacing the data we finally have:

μ = (1.5 * 2) + (2.1 * 55) / 4 (55 + 12)

μ = 133.5 / 268

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.