You place a box weighing 251.6 N on an in- clined plane that makes a 38.4◦ angle with the horizontal.
Compute the component of the gravita- tional force acting down the inclined plane.
Answer in units of N.
Check your 1-10-11,9:56am, post.
To find the component of the gravitational force acting down the inclined plane, we need to determine the weight vector of the box and then calculate its component along the direction of the inclined plane.
The weight vector is given by the formula:
Weight = mass * gravitational acceleration
Where,
Weight is the gravitational force acting on the box,
mass is the mass of the box, and
gravitational acceleration is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.
First, since weight = mass * gravitational acceleration, we need to find the mass of the box.
The formula to calculate mass is:
mass = weight / gravitational acceleration
Given that the weight of the box is 251.6 N and the gravitational acceleration is 9.8 m/s^2, we can substitute these values into the formula:
mass = 251.6 N / 9.8 m/s^2
Calculating the mass, we get:
mass ≈ 25.6735 kg
Now, we can calculate the component of the gravitational force acting down the inclined plane.
The formula to find the component of the weight vector along the direction of the inclined plane is:
Component = Weight * sin(angle)
Where,
Component refers to the component of the weight vector,
Weight is the gravitational force acting on the box, and
angle is the angle between the inclined plane and the horizontal.
Substituting the given values, we have:
Component = 251.6 N * sin(38.4°)
Calculating the component, we get:
Component ≈ 251.6 N * 0.6159
Component ≈ 154.95 N
Therefore, the component of the gravitational force acting down the inclined plane is approximately 154.95 N.
To compute the component of the gravitational force acting down the inclined plane, we can use trigonometry and the formula for the gravitational force:
F = m * g
Where:
F is the gravitational force
m is the mass of the object
g is the acceleration due to gravity (approximated to 9.8 m/s²)
Since the weight of the object is given as 251.6 N, we can find the mass of the object using the formula:
m = F / g
Substituting the given values, we have:
m = 251.6 N / 9.8 m/s²
Now, to find the component of the gravitational force acting down the inclined plane, we need to calculate the force parallel to the plane. This can be done using the formula:
F_parallel = F * sin(angle)
Substituting the values:
F_parallel = 251.6 N * sin(38.4°)
Using a scientific calculator or trigonometric table, we find that sin(38.4°) ≈ 0.618
Finally, we can solve for F_parallel:
F_parallel = 251.6 N * 0.618
Calculating this value, we find that the component of the gravitational force acting down the inclined plane is approximately 155.42 N.