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A block of mass is attached to one end of a spring with spring constant k. The other end of the spring is secured to a wall. The block is pushed against the spring, compressing it to a position x. When uncompressed, the end of the spring attached to the block is at a position x₀.The block-spring system is released, and the block travels along a horizontal, rough track. A graph of the total mechanical energy of the block-spring system as a function of position is shown. Which of the following statements about the block-spring system are true?

a. The force exerted on the block by the spring at x is F
b. The force exerted on the block by the spring at x=-0.02 meters is 1 Newton.
c. The block has maximum speed at x₀
d. The block has maximum speed at x=0.00 meters.
e. The block has half the initial spring potential energy at x.
f. The block has half the initial spring potential energy at x=-0.025 meters
g. The work done by friction as the block travels from x₀to x is.

User Kyle Shank
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Answer:

In a block-spring system without external forces, the block has maximum speed at the equilibrium position where potential energy is zero and all energy is kinetic. The force exerted by the spring is given by Hooke's law, F = -kx. If friction is present, it will decrease the total mechanical energy as work done against friction.

Step-by-step explanation:

The physics concept involved in this block-spring system primarily deals with the conservation of mechanical energy, spring force, kinematics, and work done by non-conservative forces such as friction. Assuming that no external forces like friction are acting on the system, the total mechanical energy (potential energy in the spring plus the kinetic energy of the block) remains constant. The force exerted by the spring on the block at any displacement x is calculated using Hooke's law, which is F = -kx, where k is the spring constant and x is the displacement from the equilibrium position.

The block has maximum speed at the point where the spring is neither compressed nor stretched; this is typically at x = x0 (or the equilibrium position). At this point, all of the spring's potential energy has been converted into kinetic energy. Speaking in terms of energy change, as the spring returns to its equilibrium position from being compressed or stretched, mechanical energy is converted from potential to kinetic, with kinetic energy peaking when potential energy is zero at equilibrium (x = 0.00 meters).

Regarding the work done by friction, if the track is rough, friction will act to convert some of the mechanical energy into thermal energy, which means the total mechanical energy of the block-spring system would decrease as the block moves from position x to position x0.

User Sweety
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