If a #3 kg# object moving at #9 m/s# slows down to a halt after moving #27 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?

Answer 1

#mu=0.15#

The work being done on the object is Work due to friction so the following equation is going to be used:

#color(white)(aaaaaaaaaaaa)#Equation (a) #W_f = DeltaKE#

We can rewrite Equation (a) if we break down both sides step-by-step to become:

#color(white)(aaaaaaaaaaaaaaaaaaa)#Equation (b) #color(white)(aaaaaa)##(mu*mg)*d*costheta = (1/2mv_f^2 - 1/2mv_i^2)#
#mu = "coefficient of kinetic friction"# #m = "mass (kg)"# #g = "acceleration due to gravity" (m/s^2)# #d = "displacement"(m)# #theta = "angle between friction and displacement"# #v_f = "velocity final"# #v_i = "velocity initial"#
Since our object stopped, its final velocity becomes #0# and therefore #"final KE"# becomes #0#. Friction and displacement are opposite one another so #cos(180^@) = -1#. Mass cancels on both sides. Rearrange, plug in, and solve.
#-mu*g*d= - 1/2v_i^2#
#mu=(0.5*9^2)/(9.8*27) = 40.5/264.6 = 0.15#

Answer: 0.15

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 coefficient of kinetic friction can be calculated using the formula:

[ f_k = \frac{m \cdot g \cdot d}{m \cdot v^2} ]

Where:

  • ( m ) is the mass of the object (3 kg),
  • ( g ) is the acceleration due to gravity (9.8 m/s²),
  • ( d ) is the distance traveled (27 m),
  • ( v ) is the initial velocity of the object (9 m/s).

Substituting the values:

[ f_k = \frac{3 \times 9.8 \times 27}{3 \times 9^2} ]

[ f_k = \frac{794.4}{243} ]

[ f_k ≈ 3.27 ]

Therefore, the coefficient of kinetic friction of the surface is approximately 3.27.

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