A block of mass 0.0360 kg is connected to a spring on a horizontal, frictionless

Question

A block of mass 0.0360 kg is connected to a spring on a horizontal, frictionless surface. The block is pulled 0.0400 m to the right of its equilibrium position and released. The frequency of oscillation is observed to be 14.5 Hz.

(a) Calculate the spring constant. N/m

(b) Calculate the maximum kinetic energy of the block. HINT: First find the maximum speed of the block. J

(c) What is the position (x) of the block when it has its maximum speed? (HINT: You probably don't need to do a calculation. Where is the block when it has its maximum speed?): m

(d) What is the spring (elastic) potential energy of the block when it has its greatest kinetic energy? J

(e) What is the total energy of the block? Remember that the total energy is conserved, so if you know KE + SPE at any location, you know the total energy. J

(f) What is the SPE of the block when it is 0.02 m to the right of its equilibrium position? J

(g) What is the KE of the block when it is 0.02 m to the right of its equilibrium position? (Use conservation of energy here!) J

(h) What is the velocity of the block when it is 0.02 m to the right of its equilibrium position? m/s

Explanation / Answer

(A) w = 2 pi f = 2 x pi x 14.5= 91.11 rad/s

m w^2 = k

k = (0.0360) (91.11^2) = 298.8 N/m

(b) mechanical energy = k A^2 /2 = m Vmax^2 /2

298.8 x 0.04^2 = 0.0360 Vmax^2

Vmax = 3.64 m/s

(c) x = 0

(d) PE = k x^2 / 2 = 0

(e) total energy = k A^2 /2 = (298.8)(0.04^2) / 2

= 0.24 J

(f) PE = (298.8)(0.02^2) / 2

= 0.06 J

(g) KE = 0.24 - 0.06 = 0.18 J

(h) 0.18 = 0.036 v^2 / 2

v = 3.16 m/s

(i) The block can be moving to the left or the righ

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