A 5.00 kg block (m1) is connected by means of a massless rope to a 8.40 kg block (m2). The pulley is frictionless. Calculate the maximum value for the coefficient of static friction, if the 5.00 kg block is to begin sliding.
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To calculate the maximum value for the coefficient of static friction, we need to find the conditions at which the block starts sliding.
Let's analyze the forces acting on the blocks. The force of tension (T) in the rope is the same for both blocks, and it can be expressed as:
T = m2 * g
where m2 is the mass of the second block (8.40 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, T = 8.40 kg * 9.8 m/s^2 = 82.32 N.
For the first block (m1), the weight (W1) acts downward, while the force of tension (T) acts upward. The maximum value for the coefficient of static friction (μsmax) can be defined as:
μsmax = (T - W1) / W1
Let's calculate W1. The weight (W1) can be given as:
W1 = m1 * g
where m1 is the mass of the first block (5.00 kg). So, W1 = 5.00 kg * 9.8 m/s^2 = 49 N.
Now we can calculate μsmax using the formula mentioned above:
μsmax = (T - W1) / W1
μsmax = (82.32 N - 49 N) / 49 N
μsmax = 33.32 N / 49 N
μsmax ≈ 0.68
Therefore, the maximum value for the coefficient of static friction is approximately 0.68.