Consider a block on an incline plane. The coefficients
of static and kinetic friction between
the block and the incline are µs = 0.353 and µk = 0.31.
Calculate the critical angle θc, where the block just begins to slide.
Answer in units of ◦.
The block weighs 1kg.
Please help. I don't know what to do.
all that matters is mu static
normal force = m g cos T
so Friction force = .353 m g cos T
force down slope = m g sin T
m g sin T = .353 m g cos T
tan T = .353
so if i do tan^1(.353) that should be my answer?
yes
my computer said it was wrong...
I have online hw and im stuck on this one. i tried that answer and it said it was incorrect
I get 19.4 degrees to three significant figures
that is right. thx so much bro
You are welcome.
If you can, ive got two other problems that i don't know how to do.
A block is at rest on the incline shown in
the figure. The coefficients of static and kinetic
friction are µs = 0.62 and µk = 0.53,
respectively.
The acceleration of gravity is 9.8 m/s
2
What is the largest angle which the incline
can have so that the mass does not slide down
the incline?
Answer in units of ◦
.
just realized why it was wrong the first time. I was doing tan^-1(3.53
To calculate the critical angle θc, where the block just begins to slide, we need to find the angle at which the force of gravity down the incline is equal to the maximum static friction force that can prevent the block from sliding.
Here are the steps to solve this problem:
Step 1: Find the force of gravity down the incline (Fg).
The force of gravity is given by:
Fg = m * g
where m is the mass of the block (1kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Fg = 1kg * 9.8 m/s^2
Fg = 9.8 N
Step 2: Find the maximum static friction force (Fsmax).
The maximum static friction force can be calculated using the coefficient of static friction (µs) and the normal force (N) acting on the block.
The normal force is the component of the force of gravity perpendicular to the incline, given by:
N = Fg * cos(θ)
where θ is the angle of the incline.
To calculate the maximum static friction force, we use the equation:
Fsmax = µs * N
Step 3: Set Fsmax equal to Fg and solve for θ.
Since we want to find the critical angle where the block just begins to slide, we need to find the angle at which the maximum static friction force (Fsmax) is equal to the force of gravity (Fg).
Fsmax = Fg
Substituting the equations from Steps 1 and 2:
µs * N = Fg
µs * Fg * cos(θc) = Fg
µs * cos(θc) = 1
We can solve this equation for θc by taking the inverse cosine (arccos) of both sides:
θc = arccos(1/µs)
Given that µs = 0.353, we can calculate θc:
θc = arccos(1/0.353)
Using a calculator, the critical angle θc comes out to be approximately 70.01 degrees.
Therefore, the critical angle θc, where the block just begins to slide, is approximately 70.01 degrees.