Help, please :(
A dog pulls on a pillow with a force of 6.1 N
at an angle of 27.7
◦
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.
To find the x and y components of the force, we can use trigonometry. The x component represents the horizontal component of the force, while the y component represents the vertical component.
a) To find the x component of the force, we need to find the horizontal projection of the force. We can use the formula:
x = F * cos(theta),
where F is the magnitude of the force and theta is the angle of the force with respect to the horizontal.
In this case, the magnitude of the force is 6.1 N and the angle is 27.7 degrees.
x = 6.1 N * cos(27.7 degrees).
Calculating this, we get:
x = 5.415 N (rounded to three decimal places).
Therefore, the x component of the force is 5.415 N.
b) To find the y component of the force, we need to find the vertical projection of the force. We can use the formula:
y = F * sin(theta),
where F is the magnitude of the force and theta is the angle of the force with respect to the horizontal.
In this case, the magnitude of the force is 6.1 N and the angle is 27.7 degrees.
y = 6.1 N * sin(27.7 degrees).
Calculating this, we get:
y = 2.750 N (rounded to three decimal places).
Therefore, the y component of the force is 2.750 N.
So, the answers are:
a) The x component of the force is 5.415 N.
b) The y component of the force is 2.750 N.
as always,
x = F cos(theta)
y = F sin(theta)