A box slides down a smooth plane (f=0) which is inclined at 20.0° above the horizontal. What is the acceleration of the box?
force down slope = m g sin 20 = m a
so
a = g sin 20
To find the acceleration of the box sliding down the inclined plane, we can use the following equation:
acceleration = g * sin(theta)
Where:
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- theta is the angle of the inclined plane
Given that the angle of the inclined plane is 20.0°, we can calculate the acceleration as follows:
acceleration = 9.8 m/s^2 * sin(20.0°)
Using a scientific calculator, we find:
acceleration ≈ 3.353 m/s^2
Therefore, the acceleration of the box sliding down the inclined plane is approximately 3.353 m/s^2.
To find the acceleration of the box sliding down the inclined plane, we can apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, we need to consider the forces acting on the box. The only force acting on the box as it slides down the inclined plane is its weight, which can be resolved into two components: one parallel to the inclined plane and another perpendicular to it.
The component of the weight parallel to the inclined plane is given by W sin(θ), where W is the weight of the box and θ is the angle of the inclined plane. In this case, θ is 20.0°.
So, the net force acting on the box is:
Net Force = W sin(θ)
Now, we can equate this net force to the product of the mass of the box (m) and its acceleration (a):
Net Force = m * a
Since there is no friction (f=0) mentioned in the problem, the net force is equal to the force parallel to the inclined plane:
Net Force = W sin(θ)
Therefore,
W sin(θ) = m * a
We know that the weight (W) is given by W = m * g, where g is the acceleration due to gravity. Plugging this into the equation, we have:
m * g * sin(θ) = m * a
The mass of the box (m) cancels out:
g * sin(θ) = a
Now, we can substitute the given values into the equation:
g = 9.8 m/s^2 (acceleration due to gravity)
θ = 20.0°
Plugging these values into the equation, we get:
a = 9.8 m/s^2 * sin(20.0°)
Calculating this expression, we find:
a ≈ 3.36 m/s^2
Therefore, the acceleration of the box sliding down the inclined plane is approximately 3.36 m/s^2.