How fast would a 15 kg box accelerate down a 25º snowy slope if the coefficient of kinetic friction were 0.15?

Tutors, sign in to answer this question.

Marked as Best Answer

Apply Newton's second law in the direction parallel to the incline,

mg sin25 - μmg cos25 = ma

Solve for a,

a = g(sin25 -0.15cos25) = 2.8 m/s^2 <==Answer

Hey Sun -- the 150N at 25 deg distributes 40% downhill and about 90% normal ...

the downhill 60N is opposed by 15% of the normal 135N or roughly 20N friction ...

the 40N downhill result moves the 15kg at nearly 2.7 m/s/s ... Best wishes :)

Draw a free-body diagram showing the three forces acting on the box: weight straight down, normal force perpendicular to the incline up, and friction along the incline opposite to the direction of motion.

Call the direction parallel to the incline the x-direction and the direction perpendicular to the incline the y-direction. Find the sum of all forces in the x- and y-direction:

∑F_{x}=mg sin(25) - F_{f}

∑F_{y}=F_{n}-mg cos(25)

Use Newton's 2nd law for each: in the x-direction, ∑F_{x}=ma, while in the y-direction ∑F_{y}=0.

mg sin(25) - F_{f} = ma

F_{n}- mg cos(25) =0

Get the normal force: F_{n} = mg cos(25)

Then the force of kinetic friction is: F_{f} = µ F_{n} = µ mg cos(25)

Therefore,

mg sin(25) - µ mg cos(25) = m a

Divide through by m, the answer is independent of the mass:

a = g sin(25) - µg cos(25)

a = 9.8 m/s² ( sin(25) - 0.15 cos(25) )

a = 2.8 m/s²

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Haroldo S.

Biomedical Engineer (UC Berkeley PhD) for Math and Science Tutoring

$12.50 per 15 min

View Profile >

Sanjay M.

Sanjay: Proficient tutor in physics, chemistry, SAT prep and math

$13.75 per 15 min

View Profile >

Kenneth M.

Physics and Math Tutor

$11.25 per 15 min

View Profile >