Final answer:
The crate's acceleration is approximately -2.54 m/s².
Step-by-step explanation:
To find the acceleration of the crate, we need to consider the forces acting on it. First, we calculate the gravitational force using the formula: Fg = m * g, where m is the mass of the crate and g is the acceleration due to gravity. In this case, m = 46.5 kg and g = 9.8 m/s², so Fg = 46.5 kg * 9.8 m/s² = 455.7 N.
The normal force can be determined to be equal to the gravitational force, since the crate is on a horizontal surface and not accelerating vertically. Therefore, the normal force is also 455.7 N.
The force of friction can be calculated using the formula: Ff = μk * N, where μk is the coefficient of kinetic friction and N is the normal force. In this case, μk = 0.537 and N = 455.7 N, so Ff = 0.537 * 455.7 N = 244.9 N.
Since the applied force Fa is greater than the force of friction, the crate will move. To calculate the acceleration, we use Newton's second law: Fnet = m * a, where Fnet is the net force and a is the acceleration. The net force can be calculated as the difference between the applied force and the force of friction: Fnet = Fa - Ff = 127 N - 244.9 N = -117.9 N. Since the net force is in the opposite direction of the applied force, the acceleration will be negative.
Substituting the values into the equation, we have: -117.9 N = 46.5 kg * a. Solving for a, we find that the crate's acceleration is approximately -2.54 m/s².