Question

A woman places her briefcase on the backseat of her car. As she drives to work, the car negotiates an unbanked curve in the road that can be regarded as an arc of a circle of radius 54.5 m. While on the curve, the speed of the car is 12.4 m/s at the instant the briefcase starts to slide across the backseat toward the side of the car. What force causes the centripetal acceleration of the briefcase when it is stationary relative to the car? Under what condition does the briefcase begin to move relative to the car?

Answer 1

The magnitude of the centripetal acceleration of the briefcase is 2.83 m/s^2. The force of friction causes the centripetal acceleration of the briefcase and prevents it from sliding off the seat. The briefcase begins to move relative to the car when the force of friction exceeds the maximum static friction.

Step-by-step explanation:

The magnitude of the centripetal acceleration of the briefcase can be determined using the formula:

ac = v^2 / r

Where ac is the centripetal acceleration, v is the velocity, and r is the radius of the curve. Plugging in the given values, we have:

ac = (12.4 m/s)^2 / 54.5 m = 2.83 m/s^2

The centripetal acceleration is caused by the force of friction between the briefcase and the backseat of the car. The force of friction is what prevents the briefcase from sliding off the seat and moving relative to the car. When the force of friction is less than or equal to the maximum static friction, the briefcase remains stationary relative to the car. When the force of friction exceeds the maximum static friction, the briefcase begins to slide.