A box sliding down a frictionless plane inclined at an angle 35 degrees with the horizontal. What is the acceleration of the box?
F down slope = m g sin 35
a = F/m = g sin 35 = 9.8 sin 35
To find the acceleration of the box sliding down a frictionless plane inclined at an angle of 35 degrees with the horizontal, we can use the equation:
acceleration = gravity x sin(angle)
The acceleration due to gravity, denoted as "g," is approximately 9.8 m/s^2.
First, we need to find the value of sin(35 degrees). Using a calculator or trigonometric table, we can determine that sin(35 degrees) is approximately 0.57.
Now we can calculate the acceleration:
acceleration = 9.8 m/s^2 x 0.57
acceleration ≈ 5.59 m/s^2
Therefore, the acceleration of the box sliding down the frictionless inclined plane is approximately 5.59 m/s^2.
To find the acceleration of the box sliding down the frictionless inclined plane, we can use the equations of motion. The force acting on the box along the plane is its component of the force due to gravity, which is given by:
Force along the plane = mg*sinθ
where m is the mass of the box and θ is the angle of the inclined plane.
Since there is no friction, the force along the plane is responsible for the acceleration of the box.
Now, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. So we have:
Force along the plane = m * a
where a is the acceleration of the box.
Equating the two equations, we get:
mg*sinθ = m * a
Now, we can cancel the mass 'm' from both sides of the equation:
g*sinθ = a
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the given angle θ = 35 degrees, we can calculate the acceleration using trigonometry:
a = g*sinθ = 9.8 * sin(35°)
Using a calculator, we get:
a ≈ 5.64 m/s²
Therefore, the acceleration of the box sliding down the frictionless inclined plane is approximately 5.64 m/s².