Final answer:
The block will move because the applied horizontal force exceeds the maximum static friction. Once moving, the kinetic friction force is considered to calculate acceleration, resulting in the block accelerating at approximately 3.73 m/s².
Step-by-step explanation:
To determine if the block will move under the influence of the applied force and find its acceleration, we must compare the applied force to the maximum force of static friction. The maximum force of static friction (fs_max) is calculated by multiplying the coefficient of static friction (μs) by the normal force (N). The normal force is equal to the weight of the block in this horizontal scenario, which is given as 45.0 N.
fs_max = μs * N = 0.650 * 45.0 N = 29.25 N
Since the applied force of 36.0 N is greater than the maximum static friction force of 29.25 N, the block will move. Once the block is in motion, the kinetic friction comes into play.
The force of kinetic friction (f_k) is calculated by multiplying the coefficient of kinetic friction (μk) by the normal force (N). f_k = μk * N = 0.420 * 45.0 N = 18.9 N
To calculate the acceleration (a) of the block, we use Newton's second law, subtracting the force of kinetic friction from the applied force, and divide by the mass of the block (m).
a = (applied force - f_k) / m
First, we calculate the mass (m) of the block by rearranging the weight equation (Weight = m * g) where g is the acceleration due to gravity (9.80 m/s²).
m = Weight / g = 45.0 N / 9.80 m/s² = 4.59 kg
Now, we substitute the values into the acceleration equation:
a = (36.0 N - 18.9 N) / 4.59 kg ≈ 3.73 m/s²
Therefore, the block will move, and its acceleration will be approximately 3.73 m/s².