Verizon LTE 2:31 PM session.masteringphysics.com 66% . Problem 19.28 MasteringPh

Question

Verizon LTE 2:31 PM session.masteringphysics.com 66% . Problem 19.28 MasteringPhysics A spring with spring constant 2.5× 104 N/m has a 14-kg cart at its end Part A Part complete If its amplitude of vibration is 0.030 m, what is the total energy of the cart+spring system? Express your answer to two significant figures and include the appropriate units. Utotal 11 J Submit Correct Part B What is the maximum speed of the cart? Express your answer to two significant figures and include the appropriate units. Umaz= 1 Value Units Submit Request Answer

Explanation / Answer

Given

k = 2.5*10^4 N/m

m = 1.4 kg

A = 0.030 m

at the extream end the cart has total energy is elastic potential energy and at mean position the energy is kinetic energy , at intermediate points the energy is sum of elastic potential and kinetic energy.

Part A

Total energy is E = 0.5*K*A^2 = 0.5*2.5*10^4*0.030^2 J = 11.25 J

Part B

the maximum speed will be if the mass is at its mean position where the total energy is in the form of kinetic energy only

that is 0.5*m*v^2 = 11 J

v^2 = 11*2/m

v = sqrt(11*2/1.4) m/s

v = 3.964 m/s

the maximums speed of the cart is v = 3.96 m/s

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