A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20 degrees, and the man pulls upward with a force F whose direction makes an angle of 30 degrees with the ramp. a) how large a forec F is necessary for the component F_x parallel to the ramp to be 80 N? b) How large with the component F_y then be?
I should have gotten 92.4 N for a) and 46.2N for b) Why am I getting this problem wrong? I tryed using F=mg cos theda but i keep getting the wrong answer.
80= Fcos30
Fy, perpendicular to the ramp, = Fsin30
Hi,
You may have in terms of radians instead of degree mode.
I had similar problem, but after trial and errors, I recognized it was radians instead of degrees.
So, please check your calculator, and set it up to degree mode, then you should be able to get the 92.4 N and 46.2N.
To solve this problem, we need to use trigonometry and the concept of resolving forces into components. Let's go through the steps and calculations.
a) To find the force F necessary for the component F_x parallel to the ramp to be 80 N, we can use the formula:
F_x = F * cos(30°)
Therefore, rearranging the equation:
F = F_x / cos(30°)
Substituting the given value:
F = 80 N / cos(30°)
Calculating this:
F = 80 N / 0.866
F ≈ 92.32 N
So, based on the calculations, the force F necessary for the component F_x parallel to the ramp to be 80 N is approximately 92.32 N.
b) Now, let's find the component F_y perpendicular to the ramp. We can use the formula:
F_y = F * sin(30°)
Substituting the value of F we found before:
F_y = 92.32 N * sin(30°)
Calculating this:
F_y = 92.32 N * 0.5
F_y ≈ 46.16 N
Based on the calculations, the component F_y perpendicular to the ramp is approximately 46.16 N.
If you are getting a different answer, please double-check your calculations and make sure you are using the correct values for the angles and components.
To solve this problem correctly, you need to correctly calculate the components of force F. Let's go through the process step by step:
a) To find the force component F_x parallel to the ramp, we need to use trigonometry. The formula for the cosine component is given by F_x = F * cos(theta), where theta is the angle between the force and the ramp.
You correctly identified that F_x = 80 N, and we have our angle as theta = 30 degrees. Therefore, we can rewrite the equation as:
80 N = F * cos(30 degrees)
Now, let's solve for F:
F = 80 N / cos(30 degrees)
F = 160 N
So, the required force F necessary for the component F_x parallel to the ramp to be 80 N is 160 N. It seems like you made an error while performing the trigonometric calculation, resulting in the wrong answer.
b) To find the force component F_y perpendicular to the ramp, we can now use the sine component. The formula for the sine component is given by F_y = F * sin(theta), where theta is the angle between the force and the ramp.
In this case, F_y is the force component perpendicular to the ramp, and we don't have a specific value for it. However, we can calculate it once we know the value of F.
Using the value we found in part a:
F = 160 N
theta = 30 degrees
Now, let's substitute these values into the formula:
F_y = F * sin(theta)
F_y = 160 N * sin(30 degrees)
F_y = 160 N * 0.5
F_y = 80 N
So, the component F_y is indeed 80 N, not 46.2 N as mentioned in your answer. It seems like you also made an error while calculating this component.
To summarize, the correct answers are:
a) The required force F necessary for the component F_x parallel to the ramp to be 80 N is 160 N.
b) The component F_y perpendicular to the ramp is 80 N.
Make sure to double-check your trigonometric calculations and units to avoid errors.