An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.4N ; a second force has a magnitude of 5.0N and points in the negative y direction.
Step 1: Draw a diagram to represent the situation. Label the forces and the positive x and y directions.
Step 2: Determine the directions of the forces. One force acts in the positive x direction, and the second force acts in the negative y direction.
Step 3: Assign appropriate values for the magnitudes of the forces. The magnitude of the force in the positive x direction is 6.4N, and the magnitude of the force in the negative y direction is 5.0N.
Step 4: Determine the resultant force. Since the object is moving with a constant velocity, the net force acting on the object must be zero.
Step 5: Use vector addition to find the resultant force. Start by adding the forces in the x and y directions separately.
For the x direction: There is only one force in the x direction, which is 6.4N.
For the y direction: The force in the negative y direction is 5.0N.
Step 6: Write down the components of the resultant force. The x-component of the resultant force is 6.4N, and the y-component is -5.0N.
Step 7: Calculate the magnitude and direction of the resultant force. The magnitude of the resultant force can be found using the Pythagorean theorem:
Magnitude = √(x-component^2 + y-component^2)
Magnitude = √((6.4N)^2 + (-5.0N)^2) = √((40.96N^2) + (25.0N^2)) = √(65.96N^2) = 8.12N
The direction of the resultant force can be found using trigonometry:
Direction = arctan(y-component / x-component)
Direction = arctan((-5.0N) / (6.4N)) = arctan(-0.78) = -38.7°
Step 8: Write down the final answer. The resultant force acting on the object has a magnitude of 8.12N and is directed at an angle of -38.7° from the positive x-axis.
To find the magnitude and direction of the third force acting on the object, we can use vector addition since the object is moving with constant velocity.
First, let's represent the given forces as vectors in a coordinate system:
- The force in the positive x-direction: F₁ = 6.4 N (positive x-axis)
- The force in the negative y-direction: F₂ = -5.0 N (negative y-axis)
Since the object is moving with constant velocity, the net force acting on it must be zero. Therefore, the third force acting on the object can be found by summing the two given forces:
F_net = F₁ + F₂
To do vector addition graphically, we can draw a coordinate grid and place the vectors F₁ and F₂ according to their directions and magnitudes. Then, we draw the resultant vector R, which represents the sum of F₁ and F₂. The magnitude and direction of R will represent the magnitude and direction of the unknown force.
Once we have drawn the vectors on the coordinate grid, we can use the Pythagorean theorem and trigonometry to find the magnitude and direction of R.
To find the magnitude of R, we can use the equation:
|R| = sqrt(Rx² + Ry²)
where Rx is the x-component of R and Ry is the y-component of R.
To find the direction of R, we can use the equation:
θ = tan^(-1)(Ry / Rx)
where θ is the angle that R makes with the positive x-axis.
By applying these calculations to the given vectors F₁ and F₂, we can determine the magnitude and direction of the third force acting on the object.