Class Management I Help ETA Problem Set 13 Begin Date: 11/13/2017 4:00:00 PM-Due
ID: 1787711 • Letter: C
Question
Class Management I Help ETA Problem Set 13 Begin Date: 11/13/2017 4:00:00 PM-Due Dat e: 11/202017 4:00:00 PM End Date: 128/2017 11:00:00 PM (14%) Problem 6: A small block of mass M = 250 g is placed on top of a larger block of mass 3M frictionless surface and is attached to a horizontal spring of sp the blocks is which is placed on a level ring constant k = 2.6 Nm. The coefficient of static friction between = 0.2·The lower block is pulled until the attached spring is stretched a distance D = 3.5 cm and released. Randomized Variables M=250 g D=3.5cm k = 2.6 N/m a) Assuming the blocks are stuck together, what is the maximum magnitude of acceleration amax of the blocks in variables in the problem statement? Grade Deduc Potenti max Submi Attemp (29 pe detaile Submit Hint I give up Hints: 2%, deduction per hint. Hints remaining 2 Feedback: deduction per feedback. F4 25% - Part (b) Calculate a value for the magnitude of the maximum acceleration amax of the blocks in m's" 25% Part (c) Write an equation for the . largest spring constant kmax for which the upper block does not slip 25% Part (d) Calculate a value for the largest spring constant k,nar for which the upper block does not slip, in N/m. All comen C 2017 Rxper TA, LLCExplanation / Answer
The friction force of the large object on the small object is
Ff = Mg
the accelerating force on the small object must not be larger than the friction force. Otherwise the small object will start to slip.
The maximum acceleration by this maximum force is
amax = Ff/M = Mg/M = g
the equation for the movement of the spring is
y = D*sin(t) where = (k/(M+3M)) and D = amplitude.
the acceleration a is the second derivative
v = D(k/(M+3M))*cos((k/(M+3M))
a = - D*k/(M+3M)*sin((k/(M+3M)) where the maximum acceleration is
amax = - D*k/(M+3M) = -Dk/4M
amax = -Dk/4M = -(0.035*2.6)/(4*0.25) = 0.091 m/s^2
set both equations for amax equal and solve for A:
g = - D*k/4M
kmax = 4M*g*/D = maximum spring constant
kmax = 4M*g*/D = (4*0.25*9.8*0.2)/0.035 = 56 N/m