A horizontal force of 12 N pushes a 0.50 kg book against a vertical wall. The book is initially at rest. If the coefficients of friction are \( \mu_{s} \) - 0.60 and \( \mu_{k}-0.50 \) which of the following is true? The frictional force is 7.2 N The normal force is 4.9 N If started moving downward, the block will accelerate The block will start moving and accelerate The frictional force is 4.9 N

When a horizontal force of 12 N pushes the book against the wall, it creates a normal force (N) acting outward from the wall equal to that horizontal force. So, the normal force is 12 N, not 4.9 N! With a coefficient of static friction \( \mu_{s} \) of 0.60, the maximum static friction force can be calculated as \( F_s = \mu_s \cdot N = 0.60 \cdot 12 \, \text{N} = 7.2 \, \text{N} \). Now, to address what happens if the block starts to move downwards: the gravitational force acting on the book (\( mg = 0.50 \, \text{kg} \times 9.8 \, \text{m/s}^2 \)) is 4.9 N downward. Since the static friction force (7.2 N) is greater than the downward weight, the book will not move initially; however, if it starts moving, kinetic friction will take over with a value of \( F_k = \mu_k \cdot N = 0.50 \cdot 12 \, \text{N} = 6 \, \text{N} \). In this case, the gravitational force of 4.9 N is less than the kinetic friction force of 6 N, so the book will accelerate upwards instead of downwards!