A box which has a mass of 32.8kg is placed on a plane which is inclined at 40.0° above the horizontal. The sliding friction force acting between the box and the plane is 36.4N. What is the acceleration of the box as it slides down the plane?
weight component down slope = 32.8*9.81*sin 40
net force in direction of motion = 32.8*9.81*sin 40 - 36.4
a = F/m = net force /32.8
To find the acceleration of the box as it slides down the plane, we can use Newton's second law of motion.
The force acting on the box down the inclined plane is the component of gravity parallel to the plane, which can be calculated using the formula:
Force_parallel = m * g * sin(θ)
Where:
m = mass of the box = 32.8 kg
g = acceleration due to gravity = 9.8 m/s^2 (approximate value)
θ = angle of inclination of the plane = 40.0°
Substituting the given values:
Force_parallel = 32.8 kg * 9.8 m/s^2 * sin(40.0°)
Next, we subtract the sliding friction force acting up the inclined plane:
Net_force = Force_parallel - Friction_force
Replacing the known values:
Net_force = (32.8 kg * 9.8 m/s^2 * sin(40.0°)) - 36.4 N
Finally, we use Newton's second law of motion:
Net_force = mass * acceleration
Solving for acceleration:
acceleration = Net_force / mass
Substituting the remaining values:
acceleration = ((32.8 kg * 9.8 m/s^2 * sin(40.0°)) - 36.4 N) / 32.8 kg
Calculating this expression will give us the acceleration of the box as it slides down the plane.