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Two forces act on an object. The first Force has a magnitude of 300 Newtons and acts at an angle of 30 degrees as measured from the horizontal. Second Force has a magnitude of 150 Newtons in accident angle of 135 degrees is measured from the horizontal. Determine the vector v that represents the resultant Force

Respuesta :

jushmk
This is a question of resolving the forces in question into horizontal and vertical and then finding the action of the resultant force.
The first force acts at an angle less than 90° and thus its resolved forces are positive. The second force acts at angle larger than 90° and is incident and thus its horizontal value is positive while its vertical value is negative.

Therefore;
For force of 300 N at 30°;
Horizontal value = 300*Cos 30 = 259.81 N
Vertical value = 300*Sin 30 = 150 N

For 150 N at 135°;
Horizontal value = 150*Cos (180-135) = 106.07 N
Vertical value = -150*Sin (180-135) = -106.07 N

Then,
Resultant horizontal value = 259.81+106.07 = 365.88 N
Resultant vertical value = 150-106.07 = 43.93 N

Therefore,
Resultant force, v = Sqrt (365.88^2+43.93^2) = 368.51 N
Angle of action measured from horizontal = tan ^-1(43.93/365.88) 6.85°

Then,
v = 368.51 N at 6.85° from horizontal
azikennamdi

The vector that represents the resultant Force is given as:  368.51 N at 6.85°.

What is a vector?

In the parlance of physics, a vector is a quantity that possesses magnitude as well as direction.

How can this problem be solved?

We can arrive at the solution by understanding that It's a matter of separating the forces into horizontal and vertical components and then determining the action of the resulting force.

It is to be noted that the initial force acts at a less than 90° angle, thus resulting in positive resolved forces.

Also, the second force is incident and acts at an angle greater than 90 degrees, therefore its horizontal value is positive while its vertical value is negative.

Steps to Solution

Step 1 - From the above, can surmise that:

  • Force of 300 N is given at 30°;
  • The Horizontal value is thus given as 300*Cos 30 = 259.81 N; while
  • the Vertical value is given as 300*Sin 30 = 150 N.

Step 2 - For 150 N at 135°

We have the following values:

  • Horizontal value ⇒ 150*Cos (180-135) = 106.07 N
  • Vertical value ⇒ -150*Sin (180-135) = -106.07 N

This gives us the following results:

  • Resultant horizontal value = 259.81+106.07 = 365.88 N
  • Resultant vertical value = 150-106.07 = 43.93 N

Hence,

  • the Resultant force, v = Sqrt (365.88^2+43.93^2) = 368.51 N; while
  • the Angle of action measured from horizontal = tan ^-1(43.93/365.88) 6.85°

Therefore, the Vector (v) = 368.51 N at 6.85°

Learn more about vectors at:
https://brainly.com/question/15519257
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