If a #3 kg# object moving at #20 m/s# slows to a halt after moving #500 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?

Answer 1

I got #0.04#

The only horizontal force acting on the object is kinetic friction:

#f_k=mu_kN#
where: #mu_k# is the coefficient of kinetic friction; #N# is the modulus of the Normal Reaction (of the surface); in this purely horizontal situation (no inclination or sloped surface) the normal will be equal to the weight of the object or: #N=W=mg#
We know that the object is travelling at #20m/s# when friction kicks in and slows it down to zero in #d=500 m# so we can write (from Kinematics):
#v_f^2=v_i^2+2ad# or: #0=20^2+2a*500#

giving an acceleration of:

#a=-400/(2*500)=-0.4m/s^2# negative to indicate a deceleration that will slow down our object (opposite to the direction of motion).

Finally we can use Newton's second law to equate the resultant of the forces acting on the object to mass and acceleration:

#SigmavecF=mveca#

BUT: horizontally, the only force acting on the object is friction (IN OPPOSITE DIRECTION TO THE MOTION ) so that we can write:

#-f_k=ma# #-mu_k*mg=ma#

in numbers:

#-mu_kcancel(3)*9.8=cancel(3)(-0.4)#
#mu_k=0.4/9.8=0.04#
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 equation ( \mu_k = \frac{F_{\text{friction}}}{N} ), where ( F_{\text{friction}} ) is the force of kinetic friction and ( N ) is the normal force. The normal force can be calculated as ( N = mg ), where ( m ) is the mass of the object and ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )). The force of kinetic friction can be calculated using ( F_{\text{friction}} = \mu_k \cdot N ). Given the initial velocity, final velocity, and distance traveled, you can calculate the acceleration using the equation ( v_f^2 = v_i^2 + 2a d ), where ( v_f ) is the final velocity, ( v_i ) is the initial velocity, ( a ) is the acceleration, and ( d ) is the distance. Once you have the acceleration, you can use the equation ( F_{\text{net}} = ma ) to find the net force acting on the object. The net force is the sum of the force of kinetic friction and the force due to acceleration. Rearranging the equation gives ( F_{\text{friction}} = ma - mg ). Substitute the values you have into the equations and solve for ( \mu_k ).

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