# concurrent forces

## Problem 315 | Equilibrium of Concurrent Force System

**Problem 315**

The 300-lb force and the 400-lb force shown in Fig. P-315 are to be held in equilibrium by a third force F acting at an unknown angle θ with the horizontal. Determine the values of F and θ.

## Problem 314 | Equilibrium of Concurrent Force System

**Problem 314**

The five forces shown in Fig. P-314 are in equilibrium. Compute the values of P and F.

## Problem 313 | Equilibrium of Concurrent Force System

**Problem 313**

Figure P-313 represents the concurrent force system acting at a joint of a bridge truss. Determine the value of P and E to maintain equilibrium of the forces.

## Problem 312 | Equilibrium of Concurrent Force System

**Problem 312**

Determine the magnitude of P and F necessary to keep the concurrent force system in Fig. P-312 in equilibrium.

## Problem 310 - 311 | Equilibrium of Concurrent Force System

**Problem 310**

A 300-lb box is held at rest on a smooth plane by a force P inclined at an angle θ with the plane as shown in Fig. P-310. If θ = 45°, determine the value of P and the normal pressure N exerted by the plane.

## Problem 309 | Equilibrium of Concurrent Force System

**Problem 309**

A cylinder weighing 400 lb is held against a smooth incline by means of the weightless rod AB in Fig. P-309. Determine the forces P and N exerted on the cylinder by the rod and the incline.

## Problem 308 | Equilibrium of Concurrent Force System

**Problem 308**

The cable and boom shown in Fig. P-308 support a load of 600 lb. Determine the tensile force T in the cable and the compressive for C in the boom.

## Equilibrium of Concurrent Force System

In static, a body is said to be in equilibrium when the force system acting upon it has a zero resultant.

### Conditions of Static Equilibrium of Concurrent Forces

The sum of all forces in the x-direction or horizontal is zero.

The sum of all forces in the y-direction or vertical is zero.

**Important Points for Equilibrium Forces**

## 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.

## 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.