Physics · The potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces
An ideal spring is hung vertically from the ceiling. When a mass hangs at rest f
An ideal spring is hung vertically from the ceiling. When a \( 2.0 k g \) mass hangs at rest from the spring is extended \( 6.0 \mathrm{cm} \) from its relaxed length. downward external force is now applied to the mass to extend the spring an additional 10cm. While the spring is being extended by the force, the work done by the spring is:
- A. \( -3.3 J \) \( J \)
- B. 3.3 .5
- C. \( -1.67 J \)
- D. 3.6 \( J \)
Step-by-step solution
The spring constant is determined from the initial equilibrium: k = mg/x = (2.0 kg × 9.8 m/s²) / 0.06 m = 326.67 N/m. The work done by the spring when stretching from x_i = 0.06 m to x_f = 0.16 m is W = -½k(x_f² - x_i²) = -½ × 326.67 × (0.0256 - 0.0036) = -3.59 J ≈ -3.6 J. The magnitude of this work is 3.6 J, which matches option D.
Related MCQs
- A wire suspended vertically from one of its ends is stretched by attaching a weight of to the lower end. The weight stretches the wire by 1 …
- A body is dropped from a certain height from the ground. When it is halfway down, it possess,…
- A spring is kept compressed by a toy car of mass On releasing the car it moves with a speed of So, the elastic potential energy of the sprin…
- A single conservative force \) acts on a particle that moves along the x-axis. The potential energy \) is =20+(x-2)^{2} \) where is in meter…
- Which quantity of a two particles system depend only on the separation between the two particles?…