Answer:
Approximately 32.83 Newtons of force are needed to accelerate the 4.0 kg block of wood at 6.00 m/s² along the rough surface with a coefficient of friction of 0.225.
Step-by-step explanation:
To calculate the force needed to accelerate the block of wood along the rough surface, we need to consider both the force required to overcome friction and the force required to produce the desired acceleration.
Force due to friction:
The force of friction can be calculated using the coefficient of friction (μ) and the normal force (N) acting on the block. The normal force is the force exerted by the surface perpendicular to the block's weight. On a flat surface, it is equal in magnitude but opposite in direction to the weight of the block.
The formula for the force of friction is given by:
Friction force (F_friction) = μ * N
Force needed for acceleration:
The force required to produce the desired acceleration can be calculated using Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
Force (F) = m * a
Given:
Mass of the block (m) = 4.0 kg
Acceleration (a) = 6.00 m/s²
Coefficient of friction (μ) = 0.225
We need to calculate the force needed to accelerate the block.
First, let's calculate the normal force (N):
The normal force (N) is equal to the weight of the block, which is the mass (m) multiplied by the acceleration due to gravity (g ≈ 9.81 m/s²):
N = m * g
N = 4.0 kg * 9.81 m/s² ≈ 39.24 N
Now, let's calculate the force of friction (F_friction):
F_friction = μ * N
F_friction = 0.225 * 39.24 N ≈ 8.83 N
Finally, let's calculate the total force (F_total) needed to produce the desired acceleration:
F_total = F_friction + F_acceleration
F_total = 8.83 N + (4.0 kg * 6.00 m/s²) ≈ 8.83 N + 24.00 N ≈ 32.83 N
So, approximately 32.83 Newtons of force are needed to accelerate the 4.0 kg block of wood at 6.00 m/s² along the rough surface with a coefficient of friction of 0.225.