A mass of 2 kg is attached to a spring with a spring constant of 100 N/m. It is immersed in a viscous fluid with a damping coefficient of 5 N·s/m. Calculate the damping force acting on the mass and its acceleration when displaced from equilibrium.
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To calculate the damping force acting on the mass, we can use the equation: damping force = damping coefficient × velocity.
Since the mass is displaced from equilibrium, it will experience an opposing force due to the spring. According to Hooke's Law, the spring force is given by: spring force = spring constant × displacement.
1. Damping force:
The velocity of the mass can be calculated using the equation: velocity = acceleration × time. Since the mass is not provided with an initial velocity, we can assume that the initial velocity is zero.
Given that the damping coefficient is 5 N·s/m, we can calculate the damping force:
damping force = damping coefficient × velocity = 5 N·s/m × 0 m/s
damping force = 0 N
Therefore, the damping force acting on the mass is 0 N.
2. Acceleration:
To calculate the acceleration of the mass, we can use Newton's second law: sum of forces = mass × acceleration.
The sum of forces acting on the mass includes the spring force and the damping force:
sum of forces = spring force - damping force.
Given that the spring constant is 100 N/m and the displacement is not mentioned, we cannot calculate the spring force or the acceleration accurately. We need the displacement information to calculate the acceleration.
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