4. Suppose the location of a mass on a spring (assume the mass is oscillating on

Question

4. Suppose the location of a mass on a spring (assume the mass is oscillating on a frictionles horizontal surface) is given by the following graph. Assume the units for the y-axis is cm. Characterize the dynamics of the system by answering the questions below (multiple ible answers here, only one is required) 1.00 r(s) -2.00L a) Identify a time for which the mass's kinctic energy is a maximum: b) Identify a time for which the mass's acceleration is a maximum: tify a time for which the elastic potential energy is a maximum: d) Identify a time for which the elastic potential energy is a minimum e) What is the amplitude of this oscillation? f) What is the linear frequency in Hz for this oscillation g) What is the angular frequency in radians/s for this oscillation? 5. Suppose we have 6.00 g of hot water at 60.0 C and 12.0 g of cold water at l00 Suppose the two were mixed in a perfect calorimeter, i.e. there was no heat loss to the environment. a) What would be the final equilibrium temperature for this mixture? Tfinal b) How much heat in calories did each gram of hot water lose? Each gram of hot water lost calories

Explanation / Answer

a)

for spring mass system velocity is maximum at equilibrium position.

Hence in this graph KE is maximum for times at which mass is at equilibrium positions.

So KE is maximum for t=0s

b)

for spring mass system acceleration is maximum when velocity is minimum.

In the graph velocity is minimum at maximum vertical distance, hence acceleration at t=.0s

c)

At maximum acceleration velocity is minimum hence KE is minimum thus elastic potential energy is maximum maximum at this point.

Thus Elastic potential energy is maximum at t= 1.0s

d)

At equilibrium point velocity is maximu hence KE is maximum and elastic potential energy is minimu.

Thus Elastic PE is minimu at t= 0.0s

e)

A=2.00cm

f)

Period =T= 4.0s

F=1/T= ¼.00= 0.25 Hz

g)

w=2f=2*3.14*0.25 = 1.57 rad/s

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