A 12 N horizontal force
pushes a block weighing 5.0 N
against a vertical wall (Fig. 6-26).The
coefficient of static friction between
the wall and the block is 0.60, and
the coefficient of kinetic friction is
0.40. Assume that the block is not
moving initially. (a) Will the block move? (b) In unit-vector notation,
what is the force on the block from the wall?
To determine if the block will move, we need to compare the force applied to the block (horizontal force) to the maximum static friction force between the block and the wall. If the applied force is greater than the maximum static friction, the block will start moving.
(a) Calculate the maximum static friction force using the equation:
Maximum static friction force (Ff) = coefficient of static friction (μs) * normal force (N)
The normal force (N) is equal to the weight of the block, so N = 5.0 N.
Ff = 0.60 * 5.0 N
Ff = 3.0 N
Since the applied force of 12 N is greater than the maximum static friction force of 3.0 N, the block will indeed move.
(b) The force on the block from the wall can be determined by subtracting the force due to friction from the applied force.
Friction force (Fk) = coefficient of kinetic friction (μk) * normal force (N)
Fk = 0.40 * 5.0 N
Fk = 2.0 N
To find the force on the block from the wall, subtract the force due to friction from the applied force:
Force from the wall = Applied force - Friction force
Force from the wall = 12 N - 2.0 N
Force from the wall = 10 N
The force on the block from the wall, in unit-vector notation, is 10 N in the negative x-direction.
To determine whether the block will move or not, we need to compare the maximum static friction force with the applied horizontal force.
(a) First, let's calculate the maximum static friction force using the formula:
Maximum static friction force = coefficient of static friction * normal force
The normal force is equal to the weight of the block, which is 5.0 N.
Maximum static friction force = 0.60 * 5.0 N
Maximum static friction force = 3.0 N
The maximum static friction force is 3.0 N.
Since the applied horizontal force is 12 N, which is greater than the maximum static friction force of 3.0 N, the block will move. So, the answer to part (a) is yes - the block will move.
(b) In unit-vector notation, the force between the block and the wall will be equal in magnitude but opposite in direction to the applied horizontal force. Therefore, the force can be represented as:
Force on the block from the wall = -12 N
In unit-vector notation, the force can be represented as:
Force on the block from the wall = -12 N * i, where i is the unit vector in the horizontal direction.
friction force: 12*.4= 4.8N
gravity force: 5N
gravity wins.