# resultant

## 239 Resultant of lift on the wing of an airplane

**Problem 239**

The 16-ft wing of an airplane is subjected to a lift which varies from zero at the tip to 360 lb per ft at the fuselage according to w = 90x^{1/2} lb per ft where x is measured from the tip. Compute the resultant and its location from the wing tip.

## 238 Finding the resultant of trapezoidal loading

**Problem 238**

The beam *AB* in Fig. P-238 supports a load which varies an intensity of 220 N/m to 890 N/m. Calculate the magnitude and position of the resultant load.

## 236 Computation of the resultant of parallel forces acting on the lever

**Problem 236**

A parallel force system acts on the lever shown in Fig. P-236. Determine the magnitude and position of the resultant.

## 228 Intercepts of the resultant force

**Problem 228**

Without computing the magnitude of the resultant, compute where the resultant of the forces shown in Fig. P-228 intersects the x and y axes.

## 015 Solving for a force and its angle and angle of two forces with given resultant

**Problem 015**

Forces F, P, and T are concurrent and acting in the direction as shown in Fig. P-015.

- Find the value of F and α if T = 450 N, P = 250 N, β = 30Â°, and the resultant is 300 N acting up along the y-axis.
- Find the value of F and α if T = 450 N, P = 250 N, β = 30Â° and the resultant is zero.
- Find the value of α and β if T = 450 N, P = 250 N, F = 350 N, and the resultant is zero.

## 014 Solving for force with given resultant

**Problem 014**

From Fig. P-014, P is directed at an angle α from x-axis and the 200 N force is acting at a slope of 5 vertical to 12 horizontal.

- Find P and α if the resultant is 500 N to the right along the x-axis.
- Find P and α if the resultant is 500 N upward to the right with a slope of 3 horizontal to 4 vertical.
- Find P and α if the resultant is zero.

## 013 Resultant of three forces with angles greater than 90 degree

**Problem 013**

Three vectors **A**, **B**, and **C** are shown in the figure below. Find one vector (magnitude and direction) that will have the same effect as the three vectors shown in Fig. P-013 below.

## 012 Resultant of two velocity vectors

**Problem 012**

Find the resultant vector of vectors **A** and **B** shown in Fig. P-012.

## 011 Resultant of three forces acting in a ring

**Problem 011**

Three ropes are tied to a small metal ring. At the end of each rope three students are pulling, each trying to move the ring in their direction. If we look down from above, the forces and directions they are applying are shown in Fig. P-011. Find the net force on the ring due to the three applied forces.

## Resultant of Parallel Force System

**Coplanar Parallel Force System**

Parallel forces can be in the same or in opposite directions. The sign of the direction can be chosen arbitrarily, meaning, taking one direction as positive makes the opposite direction negative. The complete definition of the resultant is according to its magnitude, direction, and line of action.