A block of mass m 3.53 kg is attached to a spring which is resting on a horizont

Question

A block of mass m 3.53 kg is attached to a spring which is resting on a horizontal frictionless table. The block is pushed into the spring, compressing it by 5.00 m, and is then released from rest. The spring begins to push the block back toward the equilibrium position at x = 0 m. The graph shows the component of the force (in N) exerted by the spring on the block versus the position of the block (in m) relative to equilibrium. Use the graph to answer the following questions How much work is done by the spring in pushing the block from its initial position at x_-5.00 m to x = 2.31 m? Number in What is the speed of the block when it reaches x= 2.31 m? Number 2.4 m/ s What is the maximum speed of the block? Once you khow how much wolk is done on the blo you can use the Work-EnergTheorem to find its sp Number net 2.7 m/s where K mv2 / 2 is the definition of kinetic energy

Explanation / Answer

From graph, F=-kx ,

6N = -k*-5m

k = 6/5 = 1.2 N/m

A] work done by spring = 0.5kx1^2 - 0.5kx2^2 = 0.5*1.2*((-5)^2 - 2.32^2)

= 11.77 J

B] work done = change in KE.

KE = 0.5mv^2

v = sqrt(2KE/m) = sqrt(2*11.77/3.53) = 2.58 m/s answer

c] for maximum speed, 0.5kx1^2 = 0.5mv^2

v = |x1|* sqrt(k/m)

= 5*sqrt(1.2/3.53)

= 2.915 m/s answer

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