A cup of coffee is on a table in an airplane flying at a constant altitude and a constant velocity. the coefficient of static friction between the cup and the table is 0.180. suddenly, the plane accelerates forward, its altitude remaining constant. what is the maximum acceleration that the plane can have without the cup sliding backward on the table? use g = 9.81 m/s2.

Question

Lena Franco

Physics

9 November, 19:43

A cup of coffee is on a table in an airplane flying at a constant altitude and a constant velocity. the coefficient of static friction between the cup and the table is 0.180. suddenly, the plane accelerates forward, its altitude remaining constant. what is the maximum acceleration that the plane can have without the cup sliding backward on the table? use g = 9.81 m/s2.

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Answers (1)

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Alexus · Answer 1

We know that the formula for static friction is:

Fs = μ N

where,

μ is the coefficient of static friction = 0.180

N is the normal force = weight of the cup = m g

We also know that from the Newton’s second law of motion, the formula for net force is:

Fnet = m a

where m is the mass of the cup and a is the acceleration of the cup

To prevent the cup from sliding backward, the static friction Fs must cancel out the net Force Fnet, that is:

Fnet - Fs = 0

Therefore:

m a - μ N = 0

m a = μ N

m a = μ (m g)

Cancelling m:

a = μ g

a = 0.180 (9.81 m / s^2)

a = 1.7658 m / s^2

Therefore the plane can only have an acceleration of about 1.77 m/s^2 before the cup starts to slide.