Item 5 A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ide

Question

Item 5 A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m. and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat. the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is Part A Calculate the elastic potential energy of the spring {take it to be zero for the unstretched spring) when the cat is at its highest point. Part B Calculate the kinetic energy of the cat when the cat is at its highest point. Part C Calculate the gravitational potential energy of the system relative to the lowest point of the motion when the cat is at its highest point. Part D Calculate the sum of these three energies when the cat is at its highest point.

Explanation / Answer

Let A be the amplitude =0.05 m

Here k = mg/A =4*9.8/0.05 = 784 N/m

A)

at the lowest point the spring is stretched by twice the amplitude of motion (2A). --> energy = 1/2k(2A)^2 =2k(A^2) = 3.92J
B)

at the lowest point, the cat's velocity is zero. --> kinetic energy = 0
C)

at the lowest point, the cat's potential energy is defined as zero.

D)

total energy at lowest point = 1/2k(2A)^2 + 0 + 0 = 2k(A^2) = 3.92 J

conservation of energy highest vs. lowest point: 0 + 0 + mg(2A) = 2k(A^2)

2mgA is the total energy.

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