You place a box weighing 302.1 N on an in-
clined plane that makes a 35.6� angle with the
horizontal.
Compute the component of the gravita-
tional force acting down the inclined plane.
Answer in units of N.
To compute the component of the gravitational force acting down the inclined plane, we need to find the force acting parallel to the incline, also known as the "downhill" component of the gravitational force.
We can start by breaking the force of gravity (weight) into its components. The weight of the box is given as 302.1 N, which represents the total force acting vertically downward.
Next, we need to find the "downhill" component of this force. To do this, we use trigonometry.
The "downhill" component can be found by multiplying the weight of the box (302.1 N) by the sine of the angle between the incline and the horizontal (35.6 degrees):
Downhill component = Weight * sin(angle)
Substituting the given values:
Downhill component = 302.1 N * sin(35.6 degrees)
Using a scientific calculator, we find that sin(35.6 degrees) is approximately 0.5783.
Calculating the downhill component:
Downhill component = 302.1 N * 0.5783
The downhill component of the gravitational force acting down the inclined plane is approximately 174.423 N.