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Force and Acceleration Example

Easy DifficultyFE Dynamics

A particle of known mass is accelerated by a constant net force. Find the magnitude of the net force using Newton’s second law.

Newton’s second law states that the net force on a particle equals its mass times its acceleration: \sum F = m a . In one dimension (or magnitude): F = ma . Force is in newtons (N), mass in kg, acceleration in m/s². \sum F = m a or F = ma (1D) Notation: \sum F = net force, m = mass, a = acceleration.

A block of mass 10 kg slides on a frictionless horizontal surface. A constant horizontal force is applied and the block accelerates at 3 m/s² in the direction of the force. Find: The magnitude of the net force acting on the block.

m = 10 kg a = 3 m/s^{2} Frictionless; force is constant and horizontal

\sum F = m a or F = ma (1D) F = (10) (3) = 30 N

Magnitude of net force: F = 30 N .

\sum F = ma; units: N = kg \cdot m/s^{2}