A long limp spring is hung from a beam; the spring's bottom is 660 mm above the table. A 0.50 kg cylinder is hooked to the spring's bottom while the spring hangs relaxed. When the cylinder is dropped, it turns around just above the table, where the spring's bottom had been stretched to 10 mm above the table. Calculate the spring's stiffness.
A long limp spring is hung from a beam; the spring's bottom is 660 mm above the table. A 0.50 kg cylinder is hooked to the spring's bottom while the spring hangs relaxed. When the cylinder is dropped, it turns around just above the table, where the spring's bottom had been stretched to 10 mm above the table. Calculate the spring's stiffness.
Concept:
The weight is attached to the spring in the case of a spring mass system. The restoring force acts on the weight when it is pushed from its equilibrium position. The only force acting at equilibrium is mg (mass Acceleration due to gravity). As a result, the restoring force is equal to kx (Spring constant Displacement), where k is the spring constant.
Thus,
where,
- k= spring stiffness
- m=mass of the cylinder attached to the spring
- g= acceleration due to gravity
- x= displacement of the spring
Given:
Mass of the cylinder (m)=0.50 kg
Spring's bottom above the table when no mass is attached= 660 mm
Spring's bottom stretched above the table when mass is attached= 10 mm
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