Question

What is the acceleration of the block and trolley system shown in if the coefficient of kinetic friction between the trolley and the surface is 0.04 ? What is the tension in the string? Take g = 10ms^-2 

Neglect the mass of the string

Answer 1

As the string is inextensible and the pulley is smooth the 3 kg block and the 20 kg trolley, both have same magnitude of motion to free body

Applying Newton's second law of motion to free body diagram of W = 20 kg

T − f_k = 20a   .....(i)

Now, f_k = μ_kR = μ_kmg = 0.04 × 20 × 10

= 8N

∴ T − 8 = 20a   ......(ii)

Again applying Newton's second law of motion to free body diagram of W = 3 kg we get

30 − T = 3a   .......(iii)

Adding (ii) and (iii), we get

22 = 23a

a = \(\frac{22}{23}\) = 0.96ms⁻²

From (ii), 

T = 20a + 8

T = 20 × 0.96 + 8

= 19.2 + 8

= 27.2N