A man is pulling on a rope with a force of 88N directed t an angle or 20 degrees to the horizontal. What is the x component of this force? What is the Y component of this force? Answer in units of N
This is what i did, but i don't know if its right:
x: cos(20)88=82.69 N
y: tan(20)82.69=30 N
F horizontal = 88 cos 20 N
F vertical = 88 sin 20 NOT TANGENT = 30.1 N
note for small angles tangent is close to sine but not the same
To find the x component of the force, you correctly used the formula:
x = cos(20) * 88 N
Evaluating this expression, we get:
x = cos(20) * 88 N ≈ 82.69 N
So, the x component of the force is approximately 82.69 N.
Now, to find the y component of the force, you used the formula:
y = tan(20) * 82.69 N
However, there seems to be a minor mistake in the formula. Instead, we need to use the sin function to find the y component.
The correct formula would be:
y = sin(20) * 88 N
Evaluating this expression, we have:
y = sin(20) * 88 N ≈ 30 N
So, the y component of the force is approximately 30 N.
To find the x and y components of a force, you can use the trigonometric functions cosine (cos) and sine (sin), respectively.
In this case, the man is pulling on the rope with a force of 88N directed at an angle of 20 degrees to the horizontal.
To find the x component of this force (the horizontal component), you can use the formula:
Force_x = Force * cos(angle)
Plugging in the values, we get:
Force_x = 88N * cos(20 degrees)
Force_x = 88N * 0.9397
Force_x ≈ 82.69 N
Therefore, the x component of the force is approximately 82.69 N.
To find the y component of this force (the vertical component), you can use the formula:
Force_y = Force * sin(angle)
Plugging in the values, we get:
Force_y = 88N * sin(20 degrees)
Force_y = 88N * 0.3420
Force_y ≈ 30.10 N
Therefore, the y component of the force is approximately 30.10 N.
So, the x component of the force is approximately 82.69 N, and the y component of the force is approximately 30.10 N.