An aluminum block of mass m 1 = 3.75 kg and a copper block of mass m 2 = 7.10 kg

Question

An aluminum block of mass m1 = 3.75 kg and a copper block of mass m2 = 7.10 kg are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in the figure below, where = 32.5°. (See the table below for the appropriate coefficients of friction).

(a) When they are released from rest, will they start to move?

YesNo    

(b) If the blocks move, determine the magnitude of their acceleration. (If the blocks do not move, enter 0.)
m/s2

(c) If the blocks move, determine the magnitude of the tension in the string. (If the blocks do not move, enter 0.)
N

(d) If the blocks do not move, determine the sum of the magnitudes of the forces of friction acting on the blocks. (If the blocks move, enter 0.)
N

Explanation / Answer

for m1

T = f1 = us1*m1*g*cos32.5 = 0.61*3.75*9.8 = 22.4 N

for m2

gravitational force Fg = m2*g*sin32.5=7.1*9.8*sin32.5 = 37.4 N

frictional force f2 = us2*m2*g*cos32.5 = 0.53*7.1*9.8*cos32.5 = 31.1 N

T + f > Fg

block will not move

++++++++++++++++++++

(b)

a = 0

+++++

(c)

f1x = -22.4

f2x = -31.1*cos32.5 = -26.2

f2y = 31.1*sin32.5 = +16.7

fx = f1x + f2x = -22.4-26.2 = -48.6 N

fy = 16.7

magnitude = sqrt(48.6^2+16.7^2) = 51.4 N

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