A dog pulls on a pillow with a force of 5 N at
an angle of 23.5 degrees above the horizontal
a) What is the x component of this force?
Answer in units of N.
b) What is the y component of this force?
Answer in units of N.
a. X = 5*Cos23.5 =
b. Y = 5*sin23.5 =
a) The x component of the force can be found by using the formula Fx = F * cos(theta), where F is the magnitude of the force and theta is the angle above the horizontal.
Fx = 5 N * cos(23.5 degrees) = 4.544 N
b) The y component of the force can be found using the formula Fy = F * sin(theta), where F is the magnitude of the force and theta is the angle above the horizontal.
Fy = 5 N * sin(23.5 degrees) = 2.097 N
To find the x and y component of the force, we can use trigonometry and the given angle.
a) The x component of the force can be found using the formula:
x component = force * cos(angle)
Plugging in the values:
x component = 5 N * cos(23.5 degrees)
Using a calculator:
x component = 5 N * 0.921
x component = 4.605 N (rounded to three decimal places)
Therefore, the x component of the force is approximately 4.605 N.
b) The y component of the force can be found using the formula:
y component = force * sin(angle)
Plugging in the values:
y component = 5 N * sin(23.5 degrees)
Using a calculator:
y component = 5 N * 0.389
y component = 1.945 N (rounded to three decimal places)
Therefore, the y component of the force is approximately 1.945 N.
To answer these questions, we need to break down the given force into its horizontal (x) and vertical (y) components.
a) The x component of a force is given by the equation: Fx = F * cos(θ), where F is the magnitude of the force and θ is the angle it makes with the horizontal.
In this case, the magnitude of the force is 5 N, and the angle is 23.5 degrees above the horizontal. Therefore, we can calculate the x component as:
Fx = 5 N * cos(23.5 degrees)
= 5 N * cos(0.41 radians)
≈ 4.547 N
So, the x component of the force is approximately 4.547 N.
b) The y component of a force is given by the equation: Fy = F * sin(θ), where F is the magnitude of the force and θ is the angle it makes with the horizontal.
In this case, the magnitude of the force is 5 N, and the angle is 23.5 degrees above the horizontal. Therefore, we can calculate the y component as:
Fy = 5 N * sin(23.5 degrees)
= 5 N * sin(0.41 radians)
≈ 2.072 N
So, the y component of the force is approximately 2.072 N.