An object, previously at rest, slides #5 m# down a ramp, with an incline of #pi/3 #, and then slides horizontally on the floor for another #2 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

(I really want someone to double check my work since this is one of my first physics answers)

#mu_k = 0.9622#

Let's use the ramp's top for the starting condition and its bottom for the ending condition.

#PE_i + KE_i = PE_f + KE_f + W_"fric"#

We are aware of:

#Deltay = 5m(sin(pi/3)) = (5sqrt3)/2# #KE_i = 0# #PE_i = mgDeltay = (5sqrt3mg)/2# #PE_f = 0# #W_"fric" = 5mu_kF_N = 5mu_kmgcos(pi/3)= 5/2mu_kmgcolor(white)"-"#

Thus, our formula is as follows:

#(5sqrt3mg)/2 = KE_f + 5/2mu_kmg#
We can also have another point (#f2#) at the end of the 2 meters when the block is at rest.
#PE_f + KE_f = PE_"f2" + KE_"f2" + W_"fric2"#
#PE_f, PE_"f2", and KE_"f2"# are all 0, and #W_"fric2" = 2mu_kmg#
#KE_f = 2mu_kmg#

Adding this to the initial equation results in:

#(5sqrt3mg)/2 = 2mu_kmg + 5/2mu_kmg#
#(5sqrt3)/2 = 9/2mu_k#
#mu_k = (5sqrt3)/9 = 0.9622#

Final Answer

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The kinetic friction coefficient of the material is approximately 0.1.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7