A 1.55 kg block slides with a speed of 0.910 m/son a frictionless horizontal sur

Question

A 1.55 kg block slides with a speed of 0.910 m/son a frictionless horizontal surface until it encounters a spring with a force constant of 745 N/m . The block comes to rest after compressing the spring 4.15 cm.

e kinetic energy spring potential energy, 0, the kinetic energy of the block, A, and the total mechanical energy of the system, E, or compressions of 0 cm. Enter your answers numerically separated by commas. Ua, Ka, Ea 0,0.642, 0.642 J Submit My Answers Give Up Correct Part B Find the spring potential energy, U,the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 1.00 cm. Enter your answers numerically separated by commas. Ub, Kb, Eb 3.73x10-2.0.605,0.642 J Submit My Answers Give Up Correct Part C Find the spring potential energy, U,the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 2.00 cm. Enter your answers numerically separated by commas. Uc, Kc, E: 0.149,0.493,0.642 J Submit My Answers Give Up

Explanation / Answer

here,

mass of block, m = 1.55 kg

velocity, u = 0.910 m/s

spring constant, k = 745 N/m

maximum compression in spring, x = 4.15 cm = 0.0415 m

final velocity after maximum compression, v = 0 m/s

Part C:
Compression, x = 2 cm = 0.02 m

Potential energy = 0.5 * k * x^2
Potential energy = 0.5 * 745 * 0.02^2
Potential energy = 0.149 J

From conservation of energy :
kinetic energy = potential energy stored in spring
kinetic energy = 0.149

total energy = K + U = 0.149 + 0.149 = 0.298 J

Part D:
compression, x = 3 cm = 0.03 m

Potential energy = 0.5 * k * x^2
Potential energy = 0.5 * 745 * 0.03^2
Potential energy = 0.335 J

From conservation of energy :
kinetic energy = potential energy stored in spring
kinetic energy = 0.335 J

total energy = K + U = 0.335 + 0.335 = 0.67 J

Part D:
Compression, x = 4 cm = 0.04 m

Potential energy = 0.5 * k * x^2
Potential energy = 0.5 * 745 * 0.04^2
Potential energy = 0.596 J

From conservation of energy :
kinetic energy = potential energy stored in spring
kinetic energy = 0.596 J

total energy = K + U = 0.596 + 0.596 = 1.196 J

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