A 180 N box is placed on an inclined plane that makes a 30.0° angle with the horizontal. Find the component of the weight force parallel to the plane's surface.
F = mg*sin30 = 180 * sin30 = 90 N.
To find the component of the weight force parallel to the plane's surface, we need to calculate the force of gravity acting on the box and then find the component of that force parallel to the inclined plane.
First, let's calculate the force of gravity acting on the box. The weight of an object can be calculated using the formula:
Weight = mass × gravitational acceleration
Gravitational acceleration is approximately 9.8 m/s^2 on the surface of the earth.
Given that the box has a weight of 180 N, we can rearrange the formula to solve for mass:
Weight = mass × gravitational acceleration
180 N = mass × 9.8 m/s^2
Dividing both sides of the equation by 9.8 m/s^2, we get:
mass = 180 N / 9.8 m/s^2
mass ≈ 18.37 kg
Now that we have the mass of the box, we can find the component of the weight force parallel to the inclined plane. This component is given by the formula:
Force_parallel = weight × sin(angle)
Using the angle of 30.0° and the weight of 180 N, we can calculate:
Force_parallel = 180 N × sin(30.0°)
Force_parallel ≈ 90 N
Therefore, the component of the weight force parallel to the inclined plane is approximately 90 N.
To find the component of the weight force parallel to the inclined plane's surface, we need to determine the force of gravity acting on the box and then calculate the component of that force that is parallel to the surface of the inclined plane.
The weight force acting on an object can be calculated using the formula:
Weight (W) = Mass (m) × Gravitational acceleration (g)
In this case, the weight force is equal to the product of the mass of the box and the gravitational acceleration. The mass is usually given in kilograms, and the gravitational acceleration is approximately 9.8 m/s^2.
So, to find the weight force of the box, we first need to calculate the mass. The formula for mass is:
Mass (m) = Weight (W) ÷ Gravitational acceleration (g)
Given that the weight of the box is 180 N, and the gravitational acceleration is 9.8 m/s^2, we can calculate the mass:
Mass (m) = 180 N ÷ 9.8 m/s^2
Mass (m) ≈ 18.4 kg (rounded to one decimal place)
Now that we have the mass, we can find the weight force using the formula:
Weight (W) = Mass (m) × Gravitational acceleration (g)
Weight (W) = 18.4 kg × 9.8 m/s^2
Weight (W) ≈ 180 N (approximation)
So, the weight force acting on the box is approximately 180 N.
Next, we can find the component of the weight force that is parallel to the inclined plane's surface. This can be calculated using the formula:
Force parallel = Weight × sin(angle)
In this case, the angle is given as 30.0°. Substituting the values into the formula, we get:
Force parallel = 180 N × sin(30.0°)
Using a calculator, we can find the sine of 30.0°, which is approximately 0.5.
Therefore, the component of the weight force parallel to the inclined plane's surface is:
Force parallel = 180 N × 0.5
Force parallel = 90 N
So, the component of the weight force parallel to the inclined plane's surface is approximately 90 N.