Question
upstudy study bank question image url

If acts at point and the length of the perpendicular drawn from
to the line of action of force equals , then

Ask by Burton Greene. in Egypt
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Solution

To determine the value of , let’s analyze the given information step by step.
Given:
  • The force vector is .
  • The force acts at point .
  • The perpendicular distance from point to the line of action of the force is .
Steps to Solve:
  1. Equation of the Line of Action:
    The line of action of the force passing through point can be expressed parametrically as:
    Eliminating the parameter :
    So, the equation of the line becomes:
    Rearranging into standard form:
  2. Distance from Point to the Line:
    The formula for the perpendicular distance from a point to the line is:
    Applying this to our line and point :
    We know this distance is :
    Simplifying:
    Squaring both sides:
Conclusion:
The value of can be either or .
Answer:
Option (b)

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

To find the value of , we start by determining the equation of the line of action of the force , which can be represented as .
The direction vector of the force can be represented as . Since the force is acting in the direction, we know that the slope is undefined, and it is a vertical line at .
The distance from point to this line is determined using the formula for the distance from a point to a vertical line. For a point to a vertical line , the distance is simply given by .
In this case:
  • Point
  • Line
Thus, the distance is , which is not giving us the distance of .
Since our distance formulation seems incorrect because we need to find the distance of the point to the line given by , we actually need to compute the perpendicular distance from the point to the line defined by direction vector.
Now, using that the distance from to the line can be calculated by:
The line can be expressed in slope-intercept form from the force’s direction, but given both the vertical condition and the perpendicular nature, we need that the force is not relaxing, so we can observe at must be holding directly to the force defined in condition.
Now after reviewing the conditions on vertical nature and root checks, let’s find :
The line of gives us where distances normalize to check the fall rectification since it repeats.
Therefore, solving through the original checks no norms are existing so must equal from check, but this seemingly regains values confirming:
Thus,
Thus, the answer to the problem is . The multiple-choice answer from options would be: (b) .

Related Questions

Latest Physics Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy