You place a box weighing 265.3 N on an inclined plane that makes a 39.1
◦
angle with the
horizontal.
Compute the component of the gravitational force acting down the inclined plane.
Answer in units of N.
To compute the component of the gravitational force acting down the inclined plane, we need to find the weight of the box acting in the direction of the incline.
The weight of an object can be calculated using the formula:
Weight = mass x gravitational acceleration
First, let's convert the weight given in Newtons to kilograms. Since weight is a force, we can use the formula:
Weight (in Newtons) = mass (in kilograms) x gravitational acceleration
Let's rearrange the formula to solve for mass:
mass (in kilograms) = Weight (in Newtons) / gravitational acceleration
Now, the gravitational acceleration is approximately 9.8 m/s^2. Substituting the values into the formula:
mass = 265.3 N / 9.8 m/s^2
Calculating this, we find the mass of the box to be:
mass = 27.052 kg
Next, we need to find the component of the weight acting down the inclined plane. This can be determined using the formula:
Component of weight = Weight x sin(angle)
Substituting the values into the formula:
Component of weight = 265.3 N x sin(39.1 degrees)
Calculating this, we find the component of the gravitational force acting down the inclined plane to be:
Component of weight = 265.3 N x 0.6293
Component of weight = 166.88229 N (rounded to 5 decimal places)
Therefore, the component of the gravitational force acting down the inclined plane is approximately 166.88229 N.