Max Angle of Mass on Incline Surface

[a_r_part]

Homework Statement

A brick with a mass of 2.3 kg is at rest on a rough surface that is at a slope that makes an angle
𝜃 above the horizontal, as shown in the diagram. If the slope becomes any steeper, the brick will start to slide downward along the slope. The coefficient of static friction of the brick with the surface is 0.67. What value must 𝜃 be less than for the brick to remain at rest?

Relevant Equations

mu = tan(theta)

Hello,

I've worked through the free-body diagram to compute the answer:

tan(𝜃) = 0.67
𝜃 = arctan(0.67) = 33.822...

The answer is supposed to be approximately 42. Yet, tan(42) is not 0.67, is the suggested answer wrong?

 

[PeroK]

Well, $\arcsin(0.67) = 42$ degrees. So, the answer looks wrong.

 

[berkeman]

Agreed. It looks like the suggested answer of 42° is wrong. Can you attach an image of the problem statement diagram, just in case there is something else going on?

 

[a_r_part]

Sure, here is the diagram:

Thanks.

 

[berkeman]

Okay, I think we agree the suggested answer is a typo. Can you check with your TA/Prof?

 

[a_r_part]

Sure, thanks.