A 3.0 kg block is pushed along a horizontal floor by a force F of magnitude 19 N at an angle θ = 30° with the horizontal. The coefficient of kinetic friction between the block and floor is 0.25.(a) Calculate the magnitude of the frictional force on the block from the floor.(b) Calculate the magnitude of the acceleration of the block.

Fnormal= 19sin30+mg=38.9 N

a)friction = u Fnormal = 0.25x38.9 = 9.73 N

b) a =( 19cos30 -Friction)/m
=2.24m/s/s

To calculate the magnitude of the frictional force on the block from the floor (a):

1. Start by determining the normal force acting on the block. Since the block is on a horizontal floor and is not accelerating vertically, the normal force is equal to the weight of the block. We can calculate the weight using the formula: weight = mass * gravitational acceleration.
weight = 3.0 kg * 9.8 m/s^2 = 29.4 N

2. Next, calculate the frictional force using the formula: frictional force = coefficient of friction * normal force.
frictional force = 0.25 * 29.4 N = 7.35 N

Therefore, the magnitude of the frictional force on the block from the floor is 7.35 N.

To calculate the magnitude of the acceleration of the block (b):

1. Resolve the applied force F into its horizontal and vertical components. The horizontal component is given by F * cosθ:
F_horizontal = 19 N * cos(30°) ≈ 16.43 N

2. Calculate the net horizontal force acting on the block. This force includes the applied force and the frictional force. Since the block is moving, the direction of the frictional force opposes the applied force. Therefore, the net horizontal force is given by:
net horizontal force = F_horizontal - frictional force
net horizontal force = 16.43 N - 7.35 N = 9.08 N

3. Use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net horizontal force is equal to the mass of the block multiplied by its horizontal acceleration:
net horizontal force = mass * acceleration
9.08 N = 3.0 kg * acceleration

4. Solve for the acceleration:
acceleration = 9.08 N / 3.0 kg ≈ 3.03 m/s^2

Therefore, the magnitude of the acceleration of the block is approximately 3.03 m/s^2.