You place a box with a mass of 20kg on an inclined plane that makes a 35.0° angle with the horizontal. What is the component of the gravitational force acting down the inclined plane?
Well, gravity can be a real downer sometimes! But in this case, let's break it down. When you have an inclined plane, the gravitational force can be split into two components: one parallel to the plane and one perpendicular to the plane. The component parallel to the plane is given by the formula Fpar = m * g * sin(θ), where m is the mass of the box, g is the acceleration due to gravity, and θ is the angle of the inclined plane. So, in this case, Fpar = 20 kg * 9.8 m/s^2 * sin(35°). Crunch those numbers, and you have your answer!
To find the component of the gravitational force acting down the inclined plane, we need to determine the gravitational force acting on the box and then find its component along the direction of the inclined plane.
The gravitational force acting on an object can be calculated using the formula:
F = m * g
Where:
- F is the gravitational force
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Given:
- Mass of the box (m) = 20 kg
- Angle of the incline (θ) = 35.0°
First, we need to find the gravitational force acting on the box:
F = 20 kg * 9.8 m/s^2
F = 196 N
Next, we need to find the component of this force along the direction of the inclined plane. This component can be calculated using the formula:
F_parallel = F * sin(θ)
Substituting the values:
F_parallel = 196 N * sin(35.0°)
F_parallel ≈ 112.65 N
Therefore, the component of the gravitational force acting down the inclined plane is approximately 112.65 N.
To find the component of the gravitational force acting down the inclined plane, we need to calculate the force of gravity and then determine its vertical and horizontal components.
Step 1: Calculate the force of gravity (weight):
The force of gravity is given by the equation: weight = mass × acceleration due to gravity. In this case, the mass is 20 kg and the acceleration due to gravity is 9.8 m/s².
So, weight = 20 kg × 9.8 m/s².
Weight = 196 N
Step 2: Determine the vertical component:
The vertical component of the gravitational force is equal to the weight multiplied by the sine of the angle of inclination.
Vertical component = weight × sin(angle)
Vertical component = 196 N × sin(35°).
Vertical component ≈ 112 N
Hence, the component of the gravitational force acting down the inclined plane is approximately 112 N.