A box is sliding down a frictionless plane inclined at an angle of 30° width the horizontal. What is the acceleration of the box?
Fp = mg*sin30 = Force parallel to the
incline.
a = Fp/m = mg*sin30/m = g*sin30 = 9.8*0.5 = 4.9 m/s^2.
To find the acceleration of the box sliding down the inclined plane, we can use the equation of motion. Let's break down the problem into its components.
1. Resolve the gravitational force: The force of gravity acting on the box can be resolved into two components - one parallel to the inclined plane and one perpendicular to it.
The component parallel to the inclined plane is given by: F_parallel = m * g * sin(theta), where m is the mass of the box, g is the acceleration due to gravity, and theta is the angle of the inclined plane.
2. Determine the net force: As there is no friction acting on the box, the only force accelerating it down the inclined plane is the component parallel to the inclined plane. So, the net force acting on the box is the same as F_parallel.
3. Apply Newton's second law: Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Therefore, we have F_net = m * a, where a is the acceleration we are trying to find.
Putting it all together, we have:
m * g * sin(theta) = m * a
Cancel out the mass:
g * sin(theta) = a
Finally, substitute the given values:
g = 9.8 m/s^2 (acceleration due to gravity)
theta = 30 degrees
a = 9.8 m/s^2 * sin(30 degrees)
a = 4.9 m/s^2
Therefore, the acceleration of the box sliding down the frictionless inclined plane at a 30-degree angle is 4.9 m/s^2.