1. A massless spring that does not obey Hooke's law is attached to a wall next to a frictionless

1. To find the work done by the spring force, we need to integrate the force over the displaceme

Question

1. A massless spring that does not obey Hooke's law is attached to a wall next to a frictionless horizontal surface in the usual way (see the diagram). The spring exerts a force of magnitude 3x + 4x^3 Newtons when the other end is stretched or compressed a distance x from its equilibrium position at x = 0. A block of mass 1 Kg is attached to the free end of the spring and is placed on the surface such that it can move back and forth in only one dimension. Show all work for each part without reference to any other parts. a. By doing an integral, calculate how much work is done by the spring force when the block is displaced from x=3cm to x=8cm. b. If the spring is released from rest at position x=14cm, how fast is it going when it gets to position x=2cm? Do this by identifying the formula for the potential energy, and starting from the statement that energy is conserved. c. Do part (b) using the work-energy theorem. d. Do part (b) assuming that the surface is not frictionless and that there is a constant kinetic friction force of magnitude 0.1 Newtons.

          1. A massless spring that does not obey Hooke's law is attached to a wall next to a frictionless horizontal surface in the usual way (see the diagram). The spring exerts a force of magnitude 3x + 4x^3 Newtons when the other end is stretched or compressed a distance x from its equilibrium position at x = 0. A block of mass 1 Kg is attached to the free end of the spring and is placed on the surface such that it can move back and forth in only one dimension.
Show all work for each part without reference to any other parts.
a. By doing an integral, calculate how much work is done by the spring force when the block is displaced from x=3cm to x=8cm.
b. If the spring is released from rest at position x=14cm, how fast is it going when it gets to position x=2cm? Do this by identifying the formula for the potential energy, and starting from the statement that energy is conserved.
c. Do part (b) using the work-energy theorem.
d. Do part (b) assuming that the surface is not frictionless and that there is a constant kinetic friction force of magnitude 0.1 Newtons.

1. A massless spring that does not obey Hooke's law is attached to a wall next to a frictionless horizontal surface in the usual way (see the diagram). The spring exerts a force of magnitude 3x + 4x^3 Newtons when the other end is stretched or compressed a distance x from its equilibrium position at x = 0. A block of mass 1 Kg is attached to the free end of the spring and is placed on the surface such that it can move back and forth in only one dimension.
Show all work for each part without reference to any other parts.
a. By doing an integral, calculate how much work is done by the spring force when the block is displaced from x=3cm to x=8cm.
b. If the spring is released from rest at position x=14cm, how fast is it going when it gets to position x=2cm? Do this by identifying the formula for the potential energy, and starting from the statement that energy is conserved.
c. Do part (b) using the work-energy theorem.
d. Do part (b) assuming that the surface is not frictionless and that there is a constant kinetic friction force of magnitude 0.1 Newtons.

Added by Melanie H.

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