please see the attached question A child with poor table manners is sliding his
ID: 1302825 • Letter: P
Question
please see the attached question
A child with poor table manners is sliding his 250-g dinner plate back and forth in SHM with amplitude of 0.100 m on a horizontal surface. At a point 0.06 m away from equilibrium, the speed of the plate is 0.300 m/s. a. What is the period? b. What is the displacement when the speed is 0.160 m/s? c. In the center of the dinner plate is a 10.0-g carrot slice. If the cannot slice is just on the verge of slipping at the endpoint of the path, what is the coefficient of static friction between the carrot slice and the plate?Explanation / Answer
a) v = w sqrt [ A2-x2 ] ----------------------(1)
w = v / sqrt [ A2-x2 ]
v = 0.300 m/s, x = 0.06 m, A = 0.100 m
w = 0.300 / sqrt [ 0.1002-0.062 ]
w = 3.75 rad/s
time period = 2pi / w = 1.675 s
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b) From (1)
x = sqrt [(Aw)2- (v)2 / w2 ]
= sqrt [(0.100 * 3.75)2- (0.160)2 / 3.752 ]
= 0.0904 m
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c) maximum frictional force acts on the carror when it is just about to slip.let ? be the coefficient of static friction between carrot and slice .
force of static friction on carrot = mu m g
This force must balance the force on the carrot dure to SHM which = m A w2
mu m g = m A w2
mu = A w2/ g = 0.100 * 3.752 / 9.8
= 0.143 [ static co-efficient of friction ]