A cup of coffee is sitting in an airplane flying at constant speed and altitude. Mu between cup and table is .36. The plane accelerates, maintaining constant altitude. What is the maximum acceleration that the plan can have without the cup sliding backwards?
friction force=masscoffe*a
mu*g*masscoffee=masscoffee*a
solve for a.
a = mu*g*m/m
a = mu*g
a = (.36)(9.80 m/s^2)
a = 3.528 m/s^2
Is this correct?
yes.
To determine the maximum acceleration that the plane can have without the cup sliding backward, we need to consider the force acting on the cup. In this scenario, there are two forces acting on the cup: the force of gravity pulling it downward and the force of friction between the cup and the table.
The force of gravity can be calculated using the formula F = mg, where m is the mass of the cup and g is the acceleration due to gravity (which is approximately 9.8 m/s^2).
The force of friction can be determined using the equation Ff = μN, where μ is the coefficient of friction and N is the normal force exerted on the cup. In this case, the normal force is equal to the force of gravity, N = mg.
Since the cup is not sliding backward, the maximum acceleration is the acceleration that just balances the forces acting on the cup. Therefore, we can set up the following equation:
Ff = F
μN = mg
μmg = mg (since N = mg)
μg = g
μ = 1
Now we can substitute the given coefficient of friction (μ = 0.36) back into the equation to find the maximum acceleration:
0.36 * 9.8 m/s^2 = 3.53 m/s^2
Therefore, the maximum acceleration that the plane can have without the cup sliding backward is approximately 3.53 m/s^2.