A 2.00 kg aluminum block and a 6.20 kg copper block are connected by a light str

Question

A 2.00 kg aluminum block and a 6.20 kg copper block are connected by a light string over a frictionless pulley. They sit on a steel surface, as shown in Figure P5.38, where = 30.0°.

When they are released from rest, will they start to move? Refer to Table 5.1 for the coefficients of friction.

Yes or No    

If so, determine the following. Enter a zero in each box if they do not move.

If not, determine the sum of the magnitudes of the forces of friction acting on the blocks. Enter zero if they do in fact move.
?? N

Explanation / Answer

Here,

Coefficient of friction for aluminium and steel system = 0.61
Coefficient of friction for Copper and steel system = 0.53

M1 = 2 kg
M2 = 6.2 kg
= 30.0°

PART A:

Calculating frictional Force for Each block When They are Released from rest:

Fas = uN = 0.61 * m1 *g = 0.61 * 2 * 9.8 = 11.95 N
Fcs = uN = 53 * m2 *g*cos30 = .53 * 6.2 * 9.8 * 0.86 = 27.69 N

If system is released from rest,The force exerted by block b to slide

F = m2*g*sin30 = 6.20 * 9.8 * 0.5 = 30.38

as F > Fcs Therefore systme will move

PART B:

Writing Force in x direction for Each block

For M1
T1 - Fas = ma
T1 - 11.95 = 2*a --------------------(1)

For M2,

mgsin40 - T + Fcs

T2 = mgsin30 + Fcs
T2 = 6.20 * 9.8 * 0.5 + 27.69
T2 = 58.07 N

Acceleration is common among blocks because of an inextensible string.
Therefore

T2 = M2 * a
58.07 / 6.02 = a

a = 9.6 m/s
Therefore,Eqn 1 will become

T1 = 2*a + 11.95
T1 = 31.15 N

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