While driving to work last year, I was holding my coffee mug in my left hand while changing the CD with my right hand. Then the cell phone rang, so I placed the mug on the flat part of my dashboard. Then, believe it or not, a deer ran out of the woods and on to the road right in front of me. Fortunately, my reaction time was zero, and I was able to stop from a speed of 20 m/s in a mere 50 m, just barely avoiding the deer. Later tests revealed that the static and kinetic coefficients of friction of the coffee mug on the dash are 0.50 and 0.30, respectively; the coffee and mug had a mass of 0.50 kg; and the mass of the deer was 120 kg. Did my coffee mug slide?

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lcmendozaf lcmendozaf · Answer 1 · 2019-11-03T16:05:07+01:00

Answer:

No, it did not slide

Explanation:

The acceleration of the vehicle is:

[tex]a = \frac{Vf^2-Vo^2}{2*d} =-4m/s^2[/tex]

We need to compare the friction force with the static friction force.

The magnitude of the friction force required for the mug not to slide is:

Ff = m*a = 0.5*4 = 2N

Now, the maximum static force is:

[tex]Fs = \mu s*N =\mu s*m*g=0.5*0.5*10=2.5N[/tex]

Since the maximum static force is greater than the required force, we can say that the mug didn't slide