Question

Two blocks, stacked one on top of the other, slide on a frictionless horizontal surface. The surface between the two blocks is rough, however, with a coefficient of static friction equal to 0.50. The top block has a mass of 2.6 kg, and the bottom block's mass is 4.0 kg. If a horizontal force F is applied to the bottom block, what is the maximum value F can have before the top block begins to slip?
We can start by calculating the maximum static friction force between the two blocks. This can be found using the equation:

f_max = μ * m_top * g

where f_max is the maximum static friction force, μ is the coefficient of static friction, m_top is the mass of the top block, and g is the acceleration due to gravity (9.81 m/s²).

f_max = 0.50 * 2.6 kg * 9.81 m/s²
f_max = 12.77 N

Now, we know that as long as the force F remains less than or equal to this maximum static friction force, the top block will not slip. Therefore, the maximum value F can have before the top block begins to slip is 12.77 N.

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