Given the following forces acting on an object find the net force:
2.0N[N], 10N[S], 2.0N[W], 8.0N[E]
The mass is 5.1 kg with the net force find the objects acceleration
Vectorially add 8 N [S] and 6 N [E]
The Pythagorean theorem tells you the resultant is 10 Newtons, in a direction between S and E. The direction can be obtained from the tangent of the angle.
(tan^-1 4/3 S of E)
How do i find the acceleration though
F=ma
you have the force and the mass. What's left to do?
To find the net force, we need to add up all the forces acting on the object. Each force can be represented by its magnitude and direction.
Let's break down the given forces:
1. 2.0N[N] - This force has a magnitude of 2.0N and acts in the north direction.
2. 10N[S] - This force has a magnitude of 10N and acts in the south direction.
3. 2.0N[W] - This force has a magnitude of 2.0N and acts in the west direction.
4. 8.0N[E] - This force has a magnitude of 8.0N and acts in the east direction.
To get the net force, we can consider the forces in the x-direction (East-West) and the forces in the y-direction (North-South) separately.
In the x-direction:
- The force acting towards the east is 8.0N[E].
- The force acting towards the west is 2.0N[W].
We can calculate the net force in the x-direction by subtracting the magnitude of the force acting towards the west from the magnitude of the force acting towards the east:
Net force in the x-direction = 8.0N - 2.0N = 6.0N[E]
In the y-direction:
- The force acting towards the north is 2.0N[N].
- The force acting towards the south is 10N[S].
We can calculate the net force in the y-direction by subtracting the magnitude of the force acting towards the south from the magnitude of the force acting towards the north:
Net force in the y-direction = 2.0N - 10N = -8.0N[N]
Now, we have the net force in the x-direction and y-direction: 6.0N[E] and -8.0N[N] respectively.
To find the net force, we can use the Pythagorean theorem since the x-direction and y-direction are perpendicular to each other:
Net force = √((Net force in x-direction)^2 + (Net force in y-direction)^2)
Net force = √((6.0N)^2 + (-8.0N)^2)
Net force = √(36.0N + 64.0N)
Net force = √(100.0N)
Net force = 10.0N
Now, with the net force, we can calculate the acceleration of the object using Newton's second law of motion:
acceleration = net force / mass
Given the mass of the object is 5.1 kg, we can substitute the values:
acceleration = 10.0N / 5.1 kg
acceleration ≈ 1.96 m/s^2
Therefore, the object's acceleration is approximately 1.96 m/s^2.