A block with mass m = 5.1 kg is attached to two springs with spring constants k
ID: 1506000 • Letter: A
Question
A block with mass m = 5.1 kg is attached to two springs with spring constants kleft = 31 N/m and kright = 56 N/m. The block is pulled a distance x = 0.24 m to the left of its equilibrium position and released from rest.
8)
What is the net force on the block at this time 1.02 s? (a negative force is to the left; a positive force is to the right)
N
9)
What is the total energy stored in the system?
J
10)
If the block had been given an initial push, how would the period of oscillation change?
the period would increase
the period would decrease
the period would not change
Explanation / Answer
8)
here
w = sqrt(k1 + K2) / m
w = sqrt[( 31 + 56) / 5.1] = 4.13rad/s
x = A sin (w * t – pie/2) = 0.24 * sin(4.13 *t - pie/2) (angles are in radians)
At time t = 1.02s
x = 0.115m to the right of the equilibrium position
F = -k * x = - (31 + 56) * (0.115) = - 10.005toward left
9)
Total energy = 0.5 * k x^2
= 0.5 * (31 + 56) * 0.24^2 = 2.5056 J
10)
The period would not change; it depends only on the equivalent spring constant and the mass. Instead, the amplitude would change
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