A block of mass 𝑚 = 5   kg m=5kg is placed on a rough horizontal surface. A horizontal force 𝐹 = 30   N F=30N is applied to the block. The coefficient of static friction between the block and the surface is 𝜇 𝑠 = 0.6 μ s ​ =0.6, and the coefficient of kinetic friction is 𝜇 𝑘 = 0.4 μ k ​ =0.4. (a) Will the block move? (b) If yes, find its acceleration. If not, find the frictional force acting on it. (Take 𝑔 = 10   m/s 2 g=10m/s 2 )

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We have a friction problem involving a 5 kilogram block on a rough horizontal surface. A horizontal force of 30 Newtons is applied to the block. The coefficient of static friction is 0.6, and the coefficient of kinetic friction is 0.4. We need to determine if the block will move and find the frictional force. First, we calculate the normal force. Since the surface is horizontal and there's no vertical acceleration, the normal force equals the weight of the block. Normal force N equals mass times gravity, which is 5 kilograms times 10 meters per second squared, giving us 50 Newtons. Next, we calculate the maximum static friction force. This is given by the coefficient of static friction times the normal force. The maximum static friction equals 0.6 times 50 Newtons, which gives us 30 Newtons. This is the maximum force that static friction can provide to prevent the block from moving. Now we compare the applied force with the maximum static friction force. The applied force is 30 Newtons, and the maximum static friction is also 30 Newtons. Since the applied force equals the maximum static friction force, and is not greater than it, the block will not move. The forces are perfectly balanced. Here's our final answer. Part A: Will the block move? No, the block will not move because the applied force of 30 Newtons equals the maximum static friction force of 30 Newtons. Part B: The frictional force acting on the block is 30 Newtons, which exactly balances the applied force to maintain static equilibrium.