Three Coplanar Concurrent Forces | Resultant Magnitude &
Direction Engineering Mechanics
1.Co-planar concurrent forces
Co-planar concurrent forces are forces that act on a single point and lie in
the same plane. The problem-solving strategy for these types of problems
involves several steps:
Draw a free body diagram: This is a diagram that shows all of the forces acting on an object. It
is important to include the direction and magnitude of each force.
Choose a pivot point: This is the point at which the forces are acting. It is important to choose
a point that makes the calculations as simple as possible.
Determine the moments of each force: The moment of a force is the tendency of that force to
cause a body to rotate about a specific point. It is calculated by multiplying the force by the
distance from the pivot point.
Sum the moments: The net moment is the sum of the moments of all of the forces. If the net
moment is zero, then the object is in equilibrium.
Sum the forces: The net force is the sum of all of the forces. If the net force is zero, then the
object is in equilibrium.
2.Resultant Force Magnitude Direction: A Comprehensive
Guide
This guide details how to calculate the magnitude and direction of a
resultant force when multiple co-planar, concurrent forces are acting on a
single point. The core principle relies on breaking down each force into its
horizontal and vertical components, summing those components
separately, and then using the Pythagorean theorem and trigonometry to
find the resultant.
1. Resolve Forces into Components:
The first step is to resolve each force into its x horizontal and y vertical
components. This is done using trigonometry sine and cosine based on the
angle the force makes with the horizontal axis. Remember:
, Horizontal Component H: Force * cosangle*
Vertical Component V: Force * sinangle*
As shown in the example problem, we have three forces: 200N, 400N at
45, and 600N at 60. Lets break them down:
200N: Only has a horizontal component: 200 * cos0 = 200N We assume the angle is 0
when its purely horizontal. Vertical component is 0.
400N 45:
Horizontal: 400 * cos45 = 400 * 0.707 282.8N
Vertical: 400 * sin45 = 400 * 0.707 282.8N
600N 60:
Horizontal: 600 * cos60 = 600 * 0.5 = 300N
Vertical: 600 * sin60 = 600 * 0.866 519.6N
2. Sum Horizontal Vertical Components:
Next, sum all the horizontal components to get H and all the vertical
components to get V.
H = 200 + 282.8 + 300 = 782.8N
V = 282.8 + 519.6 = 802.4N
Note: The transcript shows slight calculation differences, likely due to
rounding. It arrives at H = 95N and V = -1782N, which would indicate
different angles or force directions than described above. We are
following the main described scenario
3. Calculate Resultant Magnitude:
The magnitude of the resultant force R is calculated using the Pythagorean
theorem:
R=H+V
Using our calculated values:
R = 782.8 + 802.4 R = 612775.84 + 643845.76 R = 1256621.6 R 1121N
4. Determine Resultant Direction:
The direction of the resultant force is found using the inverse tangent
function:
** = tanV / H**
Direction Engineering Mechanics
1.Co-planar concurrent forces
Co-planar concurrent forces are forces that act on a single point and lie in
the same plane. The problem-solving strategy for these types of problems
involves several steps:
Draw a free body diagram: This is a diagram that shows all of the forces acting on an object. It
is important to include the direction and magnitude of each force.
Choose a pivot point: This is the point at which the forces are acting. It is important to choose
a point that makes the calculations as simple as possible.
Determine the moments of each force: The moment of a force is the tendency of that force to
cause a body to rotate about a specific point. It is calculated by multiplying the force by the
distance from the pivot point.
Sum the moments: The net moment is the sum of the moments of all of the forces. If the net
moment is zero, then the object is in equilibrium.
Sum the forces: The net force is the sum of all of the forces. If the net force is zero, then the
object is in equilibrium.
2.Resultant Force Magnitude Direction: A Comprehensive
Guide
This guide details how to calculate the magnitude and direction of a
resultant force when multiple co-planar, concurrent forces are acting on a
single point. The core principle relies on breaking down each force into its
horizontal and vertical components, summing those components
separately, and then using the Pythagorean theorem and trigonometry to
find the resultant.
1. Resolve Forces into Components:
The first step is to resolve each force into its x horizontal and y vertical
components. This is done using trigonometry sine and cosine based on the
angle the force makes with the horizontal axis. Remember:
, Horizontal Component H: Force * cosangle*
Vertical Component V: Force * sinangle*
As shown in the example problem, we have three forces: 200N, 400N at
45, and 600N at 60. Lets break them down:
200N: Only has a horizontal component: 200 * cos0 = 200N We assume the angle is 0
when its purely horizontal. Vertical component is 0.
400N 45:
Horizontal: 400 * cos45 = 400 * 0.707 282.8N
Vertical: 400 * sin45 = 400 * 0.707 282.8N
600N 60:
Horizontal: 600 * cos60 = 600 * 0.5 = 300N
Vertical: 600 * sin60 = 600 * 0.866 519.6N
2. Sum Horizontal Vertical Components:
Next, sum all the horizontal components to get H and all the vertical
components to get V.
H = 200 + 282.8 + 300 = 782.8N
V = 282.8 + 519.6 = 802.4N
Note: The transcript shows slight calculation differences, likely due to
rounding. It arrives at H = 95N and V = -1782N, which would indicate
different angles or force directions than described above. We are
following the main described scenario
3. Calculate Resultant Magnitude:
The magnitude of the resultant force R is calculated using the Pythagorean
theorem:
R=H+V
Using our calculated values:
R = 782.8 + 802.4 R = 612775.84 + 643845.76 R = 1256621.6 R 1121N
4. Determine Resultant Direction:
The direction of the resultant force is found using the inverse tangent
function:
** = tanV / H**
