A 13 N horizontal force pushes a block weighing 4.5 N against a vertical wall (Fig. 6-26). The coefficient of static friction between the wall and the block is 0.68, and the coefficient of kinetic friction is 0.35. Assume that the block is not moving initially. In unit-vector notation (Fx i + Fy j), what is the force on the block from the wall?
To find the force on the block from the wall, we need to consider the forces acting on the block along the horizontal and vertical directions.
First, let's consider the vertical direction. Since the block is not moving vertically, the vertical forces must balance each other. We have the weight of the block acting downward, which is given as 4.5 N. Therefore, the vertical force on the block from the wall must be equal in magnitude but opposite in direction to counteract the weight of the block. So, in the vertical direction, the force on the block from the wall (Fy) is -4.5 N (upwards).
Next, let's consider the horizontal direction. The only horizontal force acting on the block is the 13 N force pushing it against the wall. However, there is a static friction force opposing the motion between the block and the wall. According to the coefficient of static friction (μs = 0.68) provided, the maximum static friction force is given by:
maximum static friction force = coefficient of static friction * normal force
The normal force is the force exerted by the wall on the block perpendicular to the wall, which is equal in magnitude and opposite in direction to the vertical force on the block from the wall (Fy).
Therefore, the maximum static friction force is:
maximum static friction force = 0.68 * 4.5 N = 3.06 N
Since the block is not moving initially, the applied horizontal force of 13 N is less than the maximum static friction force. Therefore, the static friction force will act in the opposite direction to the applied force to prevent the block from moving. So, in the horizontal direction, the force on the block from the wall (Fx) is -13 N (to the left).
Putting all this together, the force on the block from the wall can be written as a vector in unit-vector notation:
Force on the block from the wall = -13 N i + (-4.5 N) j
Therefore, the force on the block from the wall is -13 N in the horizontal direction (to the left) and -4.5 N in the vertical direction (upwards).