You place a box weighing 243.2 N on an inclined plane that makes a 43.3
◦
angle with the
horizontal.
Compute the component of the gravitational force acting down the inclined plane.
Answer in units of N.
243.2 N * sin(43.3º)
watch your significant figures
To find the component of the gravitational force acting down the inclined plane, we need to calculate the force component parallel to the inclined plane.
The component of the gravitational force acting down the inclined plane can be found using trigonometric relations. The formula to calculate the component of the gravitational force parallel to the inclined plane is given by:
Force parallel = Weight × sin(angle)
Weight refers to the force due to gravity acting on the object, which can be calculated using the formula:
Weight = mass × gravity
In this case, the weight of the box is given as 243.2 N. We can use this value to calculate the component of the gravitational force acting down the inclined plane.
Let's assume the mass of the box is denoted by 'm' and the acceleration due to gravity is denoted by 'g'. Then the weight of the box can be calculated as:
Weight = m × g
Now we can substitute the given weight value of 243.2 N to solve for 'm × g':
243.2 N = m × g
Next, we need to use the given angle of 43.3 degrees to calculate the component of the gravitational force parallel to the inclined plane:
Force parallel = Weight × sin(angle)
Let's calculate the component of the gravitational force acting down the inclined plane step by step:
Step 1: Calculate the mass of the box
m × g = 243.2 N
m = 243.2 N / g
Step 2: Calculate the force parallel
Force parallel = Weight × sin(angle)
Force parallel = (m × g) × sin(angle)
Since we don't have the exact value of 'g' (acceleration due to gravity) in the problem statement, we can use the approximate value of 9.8 m/s^2 for 'g'.
Plugging in the given values, the calculation becomes:
Force parallel = (243.2 N / 9.8 m/s^2) × sin(43.3 degrees)
Now, let's calculate the value:
Force parallel ≈ (24.82 kg) × sin(43.3 degrees)
Force parallel ≈ 24.82 kg × 0.6821
Force parallel ≈ 16.94 N
Therefore, the component of the gravitational force acting down the inclined plane is approximately 16.94 N.
To compute the component of the gravitational force acting down the inclined plane, we need to consider the weight of the box and the angle of inclination.
The weight of an object is given by the formula:
Weight = mass × acceleration due to gravity
We can calculate the weight of the box by rearranging the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s².
Now, to find the component of the gravitational force acting down the inclined plane, we need to find the force acting in the direction of the inclined plane.
The force acting down the inclined plane can be calculated using the formula:
Force down the inclined plane = Weight × sin(angle of inclination)
Substituting the known values into the formula:
Force down the inclined plane = 243.2 N × sin(43.3°)
Calculating the value:
Force down the inclined plane ≈ 243.2 N × 0.6814
Force down the inclined plane ≈ 165.7 N
Therefore, the component of the gravitational force acting down the inclined plane is approximately 165.7 N.