(a) Friction= u * Normal
Friction= 0.25 * Normal
Normal=15*sin(40) + mg = 43.94
Friction= 0.25 * 43.94 = 10.985N
(b) 19*cos(40) - 10.985 = 0.5 N
F =ma
0.5N = 3.5kg * a
a = 0.14 m/s^2
Friction= 0.25 * Normal
Normal=15*sin(40) + mg = 43.94
Friction= 0.25 * 43.94 = 10.985N
(b) 19*cos(40) - 10.985 = 0.5 N
F =ma
0.5N = 3.5kg * a
a = 0.14 m/s^2
frictional force = coefficient of kinetic friction * normal force
The normal force is the force exerted by the floor on the block in the upward direction, which is equal to the block's weight since there is no vertical acceleration. The weight of the block is given by:
weight = mass * gravitational acceleration
So, weight = 3.5 kg * 9.8 m/s^2 = 34.3 N.
Therefore, the normal force is also 34.3 N.
Using the formula, the frictional force = 0.25 * 34.3 N = 8.575 N.
(b) The block's acceleration can be found using Newton's second law:
force = mass * acceleration
The horizontal component of the applied force is given by:
horizontal force = magnitude of force * cos(angle)
So, horizontal force = 15 N * cos(40°) ≈ 11.47 N.
The net force acting on the block in the horizontal direction is:
net force = horizontal force - frictional force
net force = 11.47 N - 8.575 N ≈ 2.895 N.
Using Newton's second law, we can calculate the acceleration:
2.895 N = 3.5 kg * acceleration
Therefore, the block's acceleration is approximately 0.827 m/s^2.
(a) Frictional force on the block from the floor:
First, we need to find the normal force on the block, which is the force exerted by the floor on the block perpendicular to the surface. This can be calculated using the weight of the block. The weight of the block is given by the formula: weight = mass * gravity. In this case, the mass of the block is 3.5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Thus, weight = 3.5 kg * 9.8 m/s^2 = 34.3 N.
The normal force is equal in magnitude but opposite in direction to the weight of the block. So, the normal force is 34.3 N, directed vertically upward.
Next, we can calculate the frictional force using the equation: frictional force = coefficient of friction * normal force.
Given that the coefficient of kinetic friction is 0.25, we can substitute the values: frictional force = 0.25 * 34.3 N = 8.575 N.
Therefore, the magnitude of the frictional force on the block from the floor is 8.575 N.
(b) Block's acceleration:
To calculate the block's acceleration, we need to consider the horizontal forces acting on the block. These forces are the applied force and the frictional force.
First, we need to find the horizontal component of the applied force. This can be determined by multiplying the magnitude of the applied force by the cosine of the angle è. In this case, the magnitude of the applied force is 15 N, and the angle è is 40°. So, the horizontal component of the applied force is 15 N * cos(40°) = 11.493 N.
Next, we can calculate the net horizontal force acting on the block. It is the difference between the horizontal component of the applied force and the frictional force. Net horizontal force = horizontal component of applied force - frictional force.
Thus, net horizontal force = 11.493 N - 8.575 N = 2.918 N.
Finally, we can calculate the acceleration using Newton's second law: net force = mass * acceleration. In this case, the mass of the block is 3.5 kg.
Therefore, 2.918 N = 3.5 kg * acceleration.
Solving for acceleration, we get acceleration = 2.918 N / 3.5 kg ≈ 0.832 m/s^2.
Thus, the magnitude of the block's acceleration is approximately 0.832 m/s^2.