the area under the force vs. distance graph is the work done to stretch the spring. How does the work depend o

Question

The area under the force vs. distance graph is the work done to stretch the spring. How does the work depend on the amount of stretch?

Answer 1

As the spring forceis directly proportional to distance or extension x,the relation F = -kx is a linear relation

The area onder graph is directly [area=(1/2) Fx ] prpportionalto x

as x increases area and work increases

Work is directly proportional to stretch

Answer 2

Work is force multiplied by displacement in the direction of force. When force is applied to the spring, the point of application of force at the end of the spring gets displaced by the amount of stretch of the spring. Hence stretch represents the displacement. Since force is not constant and is proportional to displacement, work is the average force multiplied by displacement (stretch of the spring) which is the area under the force vs. distance graph.

Answer 3

Because the force increases by F=kx (Hooke's Law) as the distance (x) increases. Remember that 'work' (mechanical work) is force exerted through a distance. The total energy is (1/2)kx².

Doug

Answer 4

my answer is momentum. Just a guess though.