A 20-kg box sits on a rough horizontal surface. When a...

A 20-kg box sits on a rough horizontal surface. When a horizontal force of $120 \mathrm{~N}$ is applied, the object accelerates at $1.0 \mathrm{~m} / \mathrm{s}^{2} .$ (a) If the applied force is doubled, the acceleration will (1) increase, but less than double; (2) also double; (3) increase, but more than double. Why? (b) Calculate the acceleration to prove your answer to part (a).

A 20-kg box sits on a rough horizontal surface. When a horizontal force of $120 \mathrm{~N}$ is applied, the object accelerates at $1.0 \mathrm{~m} / \mathrm{s}^{2} .$ (a) If the applied force is doubled, the acceleration will (1) increase, but less than double; (2) also double;
(3) increase, but more than double. Why? (b) Calculate the acceleration to prove your answer to part (a).

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Key Concepts

Frictional Force

Friction is a resistive force that acts opposite to the direction of motion, reducing the overall net force acting on an object. In problems involving motion on rough surfaces, friction is typically treated as a constant force determined by the interaction between the surfaces, which must be overcome by the applied force for the object to accelerate.

Net Force Analysis and Scaling

Determining the net force involves subtracting the frictional force from the applied force. When the applied force is increased while the friction remains constant, the net force increases by more than the proportionate increase in acceleration; thus, acceleration does not simply double but increases in a more pronounced manner. This illustrates the concept that the system's response (acceleration) to increased force is affected by the constant opposing force of friction.

Newton's Second Law

Newton's Second Law of Motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = m*a). This fundamental principle provides the basis for analyzing how the acceleration of an object changes in response to variations in applied forces and opposing forces like friction.

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