A drag line is connected to an electric motor. Crates are hooked onto the line and dragged horizontally from one location within the factory to another across a series of rollers.
There is 15° between the crate and motor and a force of 500N
Each crate has a mass of 200kg. Calculate the acceleration experienced by each crate?
To calculate the acceleration experienced by each crate, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The net force acting on the crate can be determined by resolving the force applied at an angle into its horizontal and vertical components. In this case, the force of 500N can be split into its horizontal and vertical components as follows:
Horizontal component: F_horizontal = F * cosθ
Vertical component: F_vertical = F * sinθ
where F is the force applied (500N) and θ is the angle between the crate and the motor (15°).
Now, let's calculate the horizontal component of the force applied to the crate:
F_horizontal = 500N * cos(15°)
F_horizontal ≈ 483.98N
The vertical component of the force applied to the crate can be ignored in this calculation because it is perpendicular to the direction of motion, and only the horizontal component affects acceleration.
The net force acting on the crate is equal to the horizontal component of the force applied:
net force = F_horizontal = 483.98N
Now, we can calculate the acceleration using Newton's second law of motion:
acceleration = net force / mass
acceleration = 483.98N / 200kg
acceleration ≈ 2.42 m/s²
Therefore, each crate experiences an acceleration of approximately 2.42 m/s² when being dragged horizontally from one location to another across the series of rollers.