A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of 403 N at an angle of 12.9° with the centerline of the canal. Find the sum of the two forces exerted by the horses on the barge.
F(x) = 403cos(12.9) + 403cos(12.9)
F(y) = 403sin(12.9) - 403sin(12.9)
F(x) = 806cos(12.9) = 761.56 N
F(y) = 0 N
Thus, the overall force vector would be 761.56 N at 0 degrees.
F(x) = 403cos(12.9) + 403cos(12.9)
F(y) = 403sin(12.9) - 403sin(12.9)
F(x) = 806cos(12.9) = 761.56 N
F(y) = 0 N
Thus, the overall force vector would be 761.56 N at 0 degrees.
or 7.6156kN
To find the sum of the two forces exerted by the horses on the barge, we first need to resolve the forces into their horizontal and vertical components.
First, let's calculate the horizontal component of each force:
Horizontal component = Force * cos(angle)
H1 = 403 N * cos(12.9°)
H2 = 403 N * cos(12.9°)
Next, let's calculate the vertical component of each force:
Vertical component = Force * sin(angle)
V1 = 403 N * sin(12.9°)
V2 = 403 N * sin(12.9°)
Now, we can find the sum of the horizontal and vertical components for each force:
Sum of horizontal components = H1 + H2
Sum of vertical components = V1 + V2
Finally, we can find the resultant force by using the Pythagorean theorem:
Resultant force = sqrt((Sum of horizontal components)^2 + (Sum of vertical components)^2)
Substituting the values:
Resultant force = sqrt((H1 + H2)^2 + (V1 + V2)^2)
Now, let's calculate the value of the sum of the two forces exerted by the horses on the barge.
To find the sum of the two forces exerted by the horses on the barge, we need to break down each force into its horizontal and vertical components.
Let's assume the centerline of the canal is the x-axis, and the horses exert a force at an angle of 12.9° with the centerline. The force exerted by each horse can be resolved into horizontal and vertical components using trigonometric functions.
1. Calculate the horizontal component of each force:
- Force1 = 403 N * cos(12.9°)
- Force2 = 403 N * cos(12.9°)
2. Calculate the vertical component of each force:
- Force1 = 403 N * sin(12.9°)
- Force2 = 403 N * sin(12.9°)
3. Add the horizontal components together to find the total horizontal force on the barge:
- Total horizontal force = Force1 (horizontal) + Force2 (horizontal)
4. Add the vertical components together to find the total vertical force on the barge:
- Total vertical force = Force1 (vertical) + Force2 (vertical)
5. Use the total horizontal and vertical forces to calculate the magnitude of the resultant force exerted by the horses on the barge:
- Magnitude of resultant force = sqrt((Total horizontal force)^2 + (Total vertical force)^2)
6. Finally, the sum of the two forces exerted by the horses on the barge is the magnitude of the resultant force.
You can evaluate the above calculations using a scientific calculator or any programming language that supports trigonometric functions to find the sum of the two forces exerted by the horses on the barge.