a box is sliding down a frictionless plane inclined at an angle of 30 degrees with the horizontal. what is the acceleration of the box?
ma=mgsinα
a=gsinα
To find the acceleration of the box, we need to analyze the forces acting on it. In this case, the only force acting on the box is its weight, which is given by W = mg, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, we need to decompose the weight vector into two components: one parallel to the incline and one perpendicular to the incline.
The component of the weight parallel to the incline is given by W_parallel = mg * sin(30°), where sin(30°) is equal to 0.5.
The component of the weight perpendicular to the incline is given by W_perpendicular = mg * cos(30°), where cos(30°) is equal to √3/2.
Since the plane is frictionless, the only force acting parallel to the incline is the component of the weight. Therefore, the acceleration of the box along the incline is equal to the net force acting on it divided by its mass.
The net force acting on the box along the incline is equal to W_parallel, so the acceleration is given by:
acceleration = W_parallel / m
Substituting the values, acceleration = (mg * sin(30°)) / m
acceleration = g * sin(30°)
Using the value of g = 9.8 m/s^2, the acceleration is:
acceleration = 9.8 * 0.5
acceleration = 4.9 m/s^2
Therefore, the acceleration of the box sliding down the frictionless plane inclined at an angle of 30 degrees with the horizontal is 4.9 m/s^2.
To find the acceleration of the box sliding down the inclined plane, we can use the following formula:
acceleration = gravitational force * sin(theta)
where:
- gravitational force is the force pulling the box down the plane, which is equal to the weight of the box (mass * gravity)
- theta is the angle between the plane and the horizontal (30 degrees in this case)
Step 1: Find the gravitational force:
The weight of the box is given by the formula weight = mass * gravity, where gravity is the acceleration due to gravity. Assuming the mass of the box is known, we can substitute the values and calculate the gravitational force.
Step 2: Calculate the acceleration:
Using the formula acceleration = gravitational force * sin(theta), substitute the values of the gravitational force and the angle (30 degrees) to find the acceleration.
Note: The acceleration obtained will be in the same units as the gravitational force (such as m/s^2 if the force is in Newtons and the mass is in kilograms).
Please provide the mass of the box so we can proceed with the calculation.