A 210-N box is placed on an inclined plane that makes a 40.0° angle with the horizontal. Find the component of the weight force parallel to the plane's surface.
To find the component of the weight force parallel to the plane's surface, we need to use trigonometry.
First, we need to calculate the weight force acting on the box. The weight force is given by the formula:
Weight force = mass × gravitational acceleration
The mass of the box is not given directly, but we can use the formula:
Weight force = mass × gravitational acceleration
Rearranging the formula, we can find the mass:
Mass = Weight force / gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
So, if we divide the weight force of 210 N by the gravitational acceleration of 9.8 m/s^2, we can find the mass of the box.
Mass = 210 N / 9.8 m/s^2
Now that we have found the mass of the box, we can calculate the component of the weight force parallel to the plane's surface.
The component of the weight force parallel to the plane's surface is given by:
Parallel component = weight force × sin(angle)
Substituting the weight force and the angle into the formula:
Parallel component = (mass × gravitational acceleration) × sin(angle)
Parallel component = (mass × 9.8 m/s^2) × sin(40 degrees)
Now you can multiply the mass you calculated earlier with the acceleration due to gravity (9.8 m/s^2), and then multiply it with the sine of 40 degrees to find the component of the weight force parallel to the plane's surface.