A bedroom bureau with a mass of 45 kg. including drawers and clothing, rests on the floor. (a)

step 1 quick free body diagram of the system. Applying Newton's second lot in the X and Y directions, w

A bedroom bureau with a mass of 45 kg. including drawers...

A bedroom bureau with a mass of $45 \mathrm{~kg}$. including drawers and clothing, rests on the floor. (a) If the coefficient of static friction between the bureau and the floor is $0.45$, what is the magnitude of the minimum horizontal force that a person must apply to start the bureau moving? (b) If the drawers and clothing, with $17 \mathrm{~kg}$ mass, are removed before the bureau is pushed, what is the new minimum magnitude?

Key Concepts

Static Friction

Static friction is the force that prevents two surfaces from sliding past each other when at rest. It must be overcome by an applied force in order to initiate motion. In scenarios like pushing a piece of furniture, the applied force has to exceed the maximum static frictional force to start the movement.

Normal Force

The normal force is the perpendicular force exerted by a surface on an object resting on it. On a horizontal surface, it is generally equal to the weight of the object (mass multiplied by gravitational acceleration). This force is critical in friction calculations since the frictional force is proportional to the normal force.

Coefficient of Static Friction

The coefficient of static friction is a dimensionless constant that quantifies the maximum static frictional force relative to the normal force. It characterizes the interaction between the surfaces in contact and is used to determine how much force is needed to overcome static friction and initiate motion.

Force Calculation in Friction Problems

When an object is at rest on a horizontal surface, the minimum horizontal force required to start its movement is calculated by multiplying the coefficient of static friction by the normal force (which is the product of mass and gravitational acceleration). Changes in the mass directly alter the normal force and, consequently, the frictional force that needs to be overcome.

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