Learning Objective: Use of the rigid body acceleration analysis. I don\'t like c

Question

Learning Objective: Use of the rigid body acceleration analysis. I don't like coffee myself, but my daughter loves Starbucks coffee. If I buy her a vanilla latte in a cup that is 5 inches deep and 3.2 inches in diameter at the top and uncovered, and then I accelerate the car away from the drive-through window at 3.2 ft/s^2, how full can the cup be and still avoid having coffee spill into her lap if she hold the cup horizontally? In other words, what is the minimum distance from the top of the cup to the coffee level required to avoid spilling if the acceleration is 3.2 ft/s^2? For simplicity, you may model the cup as if it were had a square cross- section 3.2 inches on a side. Extra thought problem: Would the assumption of a square cross-section put an upper or lower bound on your acceleration estimate for a standard round cup cross-section?

Explanation / Answer

When the car accelerates, the top surface of liquid coffee will tilt. It will tilt in such a way that the resultant force(pseudo force in the backward direction+ the gravitational force) on any particle of coffee on the surface is perpendicular to the surface. Therefore tan(tilt angle)= (acceleration of the car/g)=3.2/32=0.1

tan(tilt angle)=(minimumum distance from top of the cup/diameter of the cup)=0.1

therefore minimumum distance from top of the cup=0.1*3.2 inches =0.32 inches

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