Question

A washing machine of mass m = 80 kg has an unbalance that creates a harmonic force of magnitude F. A spring-damper system is designed to minimize the force transmitted to the base of the machine. The spring is having a stiffness coefficient k 350000 N/m. Calculate the required damping coefficient c, [N.s/m), so that only 15% of the generated force F is transmitted to the ground when the machine is running at 4500 rpm.

A. 1305.74
B. 6862.08
C. 3528.28
D. 5556.34

Answer 1

To calculate the required damping coefficient, we need to determine the force transmitted to the ground when the machine is running and the force created by the unbalance. By rearranging the equation, we can solve for the damping coefficient (c) by using the equation: c = (Force transmitted - Force created by the unbalance) / VTherefore, the correct option is: A. 1305.74

Step-by-step explanation:

To calculate the required damping coefficient, we need to determine the force transmitted to the ground when the machine is running and the force created by the unbalance. First, let's find the force created by the unbalance.

Given:

• Mass of the washing machine (m) = 80 kg
• Magnitude of the harmonic force (F)

Since we know that only 15% of the generated force F is transmitted to the ground, we can calculate the force transmitted by multiplying F by 0.15:

Force transmitted = 0.15F

Now, let's calculate the force created by the unbalance:

Force created by the unbalance = m * g

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Finally, the force transmitted to the ground is equal to the sum of the force created by the unbalance and the force generated by the spring-damper system:

Force transmitted = Force created by the unbalance + Force generated by the spring-damper system

By rearranging the equation, we can solve for the damping coefficient (c):

c = (Force transmitted - Force created by the unbalance) / VTherefore, the correct option is: A. 1305.74