Question

a 2kg aluminum block and a6kg copper block are connected by alight string over a frictionless pulley and fixed steel block of angle 30 degree .if the coefficient of friction on the surface is 0.2,find the acceleration of the two block and the tension in the string?

Answer 1

(a) The acceleration of the two block is determined as 0.93 m/s².

(b) The tension in the string is 5.78 N.

Net force on the aluminum block

The net force on the aluminum block is calculated as follows;

$T - \mu_a m_a g = m_a a \ --- \ (1)$

Net force on the copper block

The net force on the copper block is calculated as follows;

$m_cg sin(30) - T -\mu _cm_c gcos(30) = m_c a --- (2)$

where;

• T is tension in the string
• ma is mass of aluminum
• mc is mass of copper
• g is acceleration due to gravity

Solve for T using (1) and (2)

$a = g(\frac{m_c sin30\ - \ \mu _c m_c cos30 \ - \mu_ a m_a}{ma_a + m_c} )\\\\a = 9.8(\frac{6 sin30\ - \ 0.2 (6) cos30 \ - 0.2 (6)}{2 +6} )\\\\a = 0.93 \ m/s^2$

Tension in the string

From equation (1);

T = μm_ag + m_aa

T = 0.2(2)(9.8) + 2(0.93)

T = 5.78 N

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