Two blocks A and B are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on the upper block B, so that A and B move without separation is 49N. The coefficient of friction between A and B is
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Maximum force without slipping is $μ (mA+mB)g$ when masses are equal? Actually $F = μ g(mA+mB)$.
To find the coefficient of friction (\(\mu\)) between blocks A and B, we need to consider the condition for the maximum horizontal force applied on the upper block B without causing separation between A and B. The given maximum force is 49 N.
The force of friction that prevents the separation is given by the formula:
\(f_{\text{max}} = \mu \times N\)
where \(N\) is the normal force. Since the system is on a smooth horizontal surface, \(N\) is equal to the weight of block B, which can be calculated as:
\(N = m_B \times g\)
Given that the mass of block B is 3 kg and the acceleration due to gravity \((g)\) is 9.8 m/s², we have:
\(N = 3 \times 9.8 = 29.4 \text{ N}\)
The maximum force of friction that can act is the same as the given maximum horizontal force, which is 49 N:
\(f_{\text{max}} = 49 \text{ N}\)
Setting the expression for the frictional force equal to the applied force:
\(\mu \times 29.4 = 49\)
Solving for \(\mu\):
\(\mu = \frac{49}{29.4} = 1.666 \approx 0.5\)
Thus, the coefficient of friction between A and B is 0.5.
