You place a box weighing 251.6 N on an in- clined plane that makes a 38.4◦ angle with the horizontal.
Compute the component of the gravita- tional force acting down the inclined plane.
Answer in units of N.
Fp = 251.6sin38.4 = 156.3N. = Force
acting down the inclined plane.
To compute the component of the gravitational force acting down the inclined plane, we can use trigonometry. The gravitational force can be broken down into two components: one parallel to the inclined plane (known as the parallel component) and one perpendicular to the inclined plane (known as the perpendicular component).
The parallel component of the gravitational force is given by the equation F_parallel = m * g * sin(theta), where m is the mass of the object being considered, g is the acceleration due to gravity (approximately 9.8 m/s^2), and theta is the angle between the inclined plane and the horizontal.
In this case, the weight of the box is given as 251.6 N. Since weight = mass * acceleration due to gravity, we can rearrange the equation to find the mass, m = weight / g.
Calculating the mass:
m = 251.6 N / 9.8 m/s^2 ≈ 25.67 kg
Now, we can compute the parallel component of the gravitational force:
F_parallel = m * g * sin(theta)
F_parallel = 25.67 kg * 9.8 m/s^2 * sin(38.4 degrees)
F_parallel ≈ 25.67 kg * 9.8 m/s^2 * 0.6153
F_parallel ≈ 154.14 N
Therefore, the component of the gravitational force acting down the inclined plane is approximately 154.14 N.