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If an object with a mass of #10 kg # is moving on a surface at #15 m/s# and slows to a halt after # 4 s#, what is the friction coefficient of the surface?

Answer 1

Lily Adams

The coefficient of friction is #=0.38#

We start by calculating the deceleration.

We apply the equation of motion

#v=u+at#

The initial velocity is #u=15ms^-1#

The time is #t=4s#

The final velocity is #v=0ms^-1#

Therefore,

#0=15+4a#

The acceleration is

#a=-15/4ms^-2#

According to Newton's Second Law, the frictional force is #F_r=ma#

So,

#F_r=10*15/4=75/2N#

The normal force is

#N=mg=10*9.8=98N#

The coefficient of friction is

#mu_k=F_r/N=37.5/98=0.38#

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Answer 2

Adam Arnold

The friction coefficient of the surface can be calculated using the equation: friction force = friction coefficient × normal force. First, calculate the initial kinetic energy of the object using the formula KE = 0.5 × mass × velocity^2. Then, find the work done by friction using the formula W = force × distance, where distance = velocity × time. Finally, equate the work done by friction to the initial kinetic energy and solve for the friction coefficient using the equation W = μ * N, where N is the normal force. With the given information, the friction coefficient can be determined.

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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.