Sapling Learning A block of mass m 3.98 kg is attached to a spring which is rest

Question

Sapling Learning A block of mass m 3.98 kg is attached to a spring which is resting on a horizontal frictionless table. The block is pushed into the compressing it by 5.00 m, and is then released from rest. The spring ns to push the block back toward the equilibrium position at x 0m. 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 6 Number 4 2 What is the speed of the block when it reaches x-2.97 m? r(m Number m/s What is the maximum speed of the block? Number m/s Hint Previous Give Up& View Solution

Explanation / Answer

spring constant = k = slope of the graph f and x = 6/5= 1.2 N/m.

a)

Work done = 1/2*kx^2

Work done ( -5 , 2.97 ) = 0.5 x1.2 x ( 25 - 8.8209 ) = 9.71 J

b)

using machanical energy conversion,

1/2*k*5^2 + 0 = 1/2*k*2.97^2 + 1/2mv^2

v = sqrt[2/m (1/2*k(5^2 - 2.97^2)

v = = sqrt[2/3.98 (1/2*1.2(5^2 - 2.97^2)

v = 2.21 m/s

c)

maxmium speed of the block when force on block is zero

1/2*k*5^2 + 0 = 1/2k*(0)^2 + 1/2mv^2

v = sqrt(k*5^2 / m)

v = sqrt[(1.2 x 5^2) / 3.98]

v = 2.75 m/s^2

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