You place a box weighing 242.4 N on an inclined plane that makes a 37.2◦
angle with the horizontal.
Compute the component of the gravitational force acting down the inclined plane.
Answer in units of N.
Please
242.4 N * sin(37.2º)
Well, gravity certainly has a way of bringing us down, doesn't it? In this case, we need to find the component of the gravitational force acting down the inclined plane. Let's do some math and see what we can come up with.
First, we'll find the component of the gravitational force parallel to the plane. To do that, we need to multiply the weight of the box (242.4 N) by the sine of the angle of the inclined plane (37.2°).
So, the component of the gravitational force acting down the inclined plane is given by:
242.4 N * sin(37.2°) = 145.3 N (approximately)
So, the component of the gravitational force acting down the inclined plane is approximately 145.3 N.
To compute the component of the gravitational force acting down the inclined plane, we need to find the vertical and horizontal components of the gravitational force.
The vertical component of the gravitational force can be calculated using the formula:
F_vertical = F * sin(theta)
Where:
F = weight of the box = 242.4 N
theta = angle of the inclined plane = 37.2°
Therefore, the vertical component of the gravitational force is:
F_vertical = 242.4 N * sin(37.2°)
F_vertical = 242.4 N * 0.6018
F_vertical ≈ 145.84 N (rounded to two decimal places)
So, the component of the gravitational force acting down the inclined plane is approximately 145.84 N.
To compute the component of the gravitational force acting down the inclined plane, we need to consider the weight of the box and the angle of the inclined plane.
The weight of the box is given as 242.4 N, which represents the force due to gravity acting vertically downward. We need to determine the component of this weight that acts down the inclined plane.
To do this, we can use the concept of vector decomposition. The weight can be decomposed into two components: one that acts perpendicular to the inclined plane (normal force) and another that acts parallel to the inclined plane (component force).
The normal force acts perpendicular to the inclined plane, meaning it is equal and opposite to the component of the weight that is perpendicular to the inclined plane (which cancels out any motion in that direction). In this case, the normal force is equal to the weight component that acts perpendicular to the inclined plane.
To find the weight component parallel to the inclined plane, we need to use trigonometry. The weight component can be found using the formula:
Weight component parallel = Weight * sin(angle)
Plugging in the given values:
Weight = 242.4 N
Angle = 37.2°
Weight component parallel = 242.4 N * sin(37.2°)
Using a calculator, we can calculate the value of sin(37.2°) to be approximately 0.6018.
Weight component parallel = 242.4 N * 0.6018
Weight component parallel = 145.94712 N
Therefore, the component of the gravitational force acting down the inclined plane is approximately 145.95 N.