A 124 kg mass is pushed by an applied force of 1000 N, which causes the mass to accelerate horizontally at a rate of 4 m/s\(^2\). Determine the coefficient of kinetic friction.

The coefficient of kinetic friction is approximately 0.407. To determine the coefficient of kinetic friction, we can use Newton's second law of motion and the relationship between force, mass, and acceleration.

First, let's find the net force acting on the mass. The applied force is 1000 N. According to Newton's second law (F = ma), the net force is equal to the product of mass and acceleration:

Net force = mass × acceleration

Net force = 124 kg × 4 m/s^2

Net force = 496 N

Now, let's consider the forces acting on the mass. There is the applied force pushing it forward, and there is the force of kinetic friction opposing its motion. The magnitude of the force of kinetic friction can be determined using the equation:

Force of kinetic friction = coefficient of kinetic friction × normal force Since the mass is moving horizontally, the normal force is equal to the weight of the mass, which can be calculated as:

Weight = mass × gravitational acceleration

Weight = 124 kg × 9.8 m/s^2

Weight = 1215.2 N

Now, substituting the values into the equation for the force of kinetic friction:

496 N = coefficient of kinetic friction × 1215.2 N

Simplifying the equation:

coefficient of kinetic friction = 496 N / 1215.2 N

coefficient of kinetic friction ≈ 0.407

Therefore, the coefficient of kinetic friction is approximately 0.407.

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