Question

(i) By giving an explanation, state whether frictional force is a conservative or

non-conservative force.

(ii) When the three blocks in Fig. 2 are released from rest, they accelerate with a

magnitude of 0.500 m/s2. Block 1 has mass M, block 2 has 2M, and block 3 has

2M. Determine the coefficient of kinetic friction between block 2 and the table.

[3,6]

Answer 1

Part(a)

Friction is a good example of a nonconservative force. As illustrated in Figure 1, work done against friction depends on the length of the path between the starting and ending points. Because of this dependence on path, there is no potential energy associated with nonconservative forces.

Part (b)

Let the tension on the string connecting M₂,M₃be T₂₃ and that connection M₂,M₁be T₁₂ respectively apply

Newton's second law

$M_3g-T3g=M_3a$

$T_{23}-\mu_km_2g-T_{12}=m_2a$

$T_{12}-m_1g=m_1g$

Adding up the three equation

$m_1=M,m_2=m_3=2M$

$2Mg-2\mu_kMg-Mg=5Ma$

Where

a=0.500m/sec²

$Mg-2\mu_k Mg=(5\times0.500)M$

$g(1-2\mu_k)=2.5$

$1-2\mu_k=\frac{2.5}{9.8}$

$\mu_k=0.37$