Physics

Physics

Problem

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.250.25 (g=10 m s−2g = 10 \text{ m s}^{-2})
Intuitive explanation

The key is recognizing that friction is the only horizontal force available to accelerate the body along with the car. The maximum acceleration occurs when static friction reaches its limit—when the friction force equals μsN\mu_s N. Set up Newton's second law for the body in the car's reference frame (or the ground frame), equate the maximum friction force to mama, and solve for aa. The normal force equals the body's weight since there's no vertical acceleration.

Intuitive explanation

The key is recognizing that friction is the only horizontal force available to accelerate the body along with the car. The maximum acceleration occurs when static friction reaches its limit—when the friction force equals μsN\mu_s N. Set up Newton's second law for the body in the car's reference frame (or the ground frame), equate the maximum friction force to mama, and solve for aa. The normal force equals the body's weight since there's no vertical acceleration.

Browse the problem library