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 positive magnitude of 6.7N; a second force has a magnitude of 4.6 N and points in the negative y direction. (1)"Find magnitude of the third force acting on the object.
(2) Find the direction of the third force acting on the object in terms of pheta=-----------degrees from the + x direction.
1,2. F1+F2+F3 = M*a = M*0 = 0.
6.7 - 4.6i + F3 = 0.
F3 = -6.7 + 4.6i = 8.13 N.[34.5o] N. of W. = 145.5o CCW from +x-axis.
To find the magnitude of the third force acting on the object, we can use vector addition. Since the object is moving with constant velocity, the net force acting on it must be zero. Therefore, the magnitudes of the three forces must add up to zero.
Let's denote the magnitude of the third force as F3. We know that the magnitude of the first force is 6.7 N, and the magnitude of the second force is 4.6 N. Given that the forces are acting in different directions, we can write the equation:
6.7 N + 4.6 N + F3 = 0
Simplifying the equation, we get:
F3 = -6.7 N - 4.6 N
F3 = -11.3 N
Therefore, the magnitude of the third force acting on the object is 11.3 N.
To find the direction of the third force, we need to determine the angle theta (θ) it makes with the positive x direction. We can use trigonometry to find this angle.
Given that the first force is in the positive x direction, we can say that its angle with the x-axis is 0 degrees. Since the second force is in the negative y direction, its angle with the x-axis is 270 degrees (or -90 degrees).
Now, let's denote the angle between the third force and the x-axis as theta (θ). Using vector addition, we can find the resultant of the forces and determine the angle it makes with the x-axis.
Using the Pythagorean theorem, we can find the resultant of the forces:
R^2 = (6.7 N)^2 + (4.6 N)^2
Solving for R, we get:
R ≈ 7.97 N
The angle theta (θ) can be found using the inverse tangent function:
θ = arctan(4.6 N / 6.7 N)
Calculating this value using a calculator, we find:
θ ≈ 35.3 degrees
Therefore, the direction of the third force acting on the object is approximately 35.3 degrees from the positive x direction.
To find the magnitude of the third force acting on the object, you will need to use vector addition. Since the object is moving with constant velocity, the net force acting on it must be zero. Therefore, the magnitude of the third force must be equal to the sum of the magnitudes of the first two forces.
(1) Magnitude of the third force = Magnitude of the first force + Magnitude of the second force
= 6.7 N + 4.6 N
= 11.3 N
So, the magnitude of the third force acting on the object is 11.3 N.
To find the direction of the third force, you can use trigonometry. Since two forces act along the x and y directions, the third force will have components along both of these directions.
Let's consider the angle theta (ϴ) that the third force makes with the positive x-direction.
(2) Direction of the third force = arctan (y-component / x-component) = arctan (-4.6 N / 6.7 N)
Calculating the value, we get:
Direction of the third force = arctan (-0.68657)
= -35.86 degrees (rounded to two decimal places)
Therefore, the direction of the third force acting on the object, in terms of theta, is approximately -35.86 degrees from the +x direction.
constant velocity means no net force. So add the three forces, and equal zero.
6.7x -4.6y + z=0
let z have two components, in the x direction, and the y direction.
then zx=-6.7x
and zy=4.6y
but zx= ZcosTheta and zy=ZsinTheta
so ZcosTheta=-6.7
ZsinTheta=4.6
which makes (dividing the first equation into the second)
tanTheta=-.687
Theta=180-34.5 degrees where theta is counterclockwise from the x axis.
Z sinTheta=4.6, so you can solve for Z