Find the size of the net force produced by a 4 N and a 14 N force in each of the following arrangements.
(a) The forces act in the same direction.
N
(b) The forces act in opposite directions.
N
(c) The forces act at right angles to each other.
N
(a) they add
(b) they subtract
(c) use Pythagoras ... a^2 + b^2 = c^2
... the resultant is the hypotenuse
To find the size of the net force produced by two forces, you need to consider the vector addition of the forces involved. The net force is the vector sum of the forces acting on an object. Let's calculate the net force in each of the given arrangements:
(a) The forces act in the same direction:
To find the net force, we simply add the magnitudes of the forces. In this case, the net force is equal to the sum of the magnitudes of the forces.
Net force = 4 N + 14 N = 18 N.
Therefore, the net force produced by the 4 N and 14 N forces acting in the same direction is 18 N.
(b) The forces act in opposite directions:
In this case, we need to subtract the magnitudes of the forces to find the net force. The direction of the net force will be the same as the larger force.
Net force = 14 N - 4 N = 10 N.
Therefore, the net force produced by the 4 N and 14 N forces acting in opposite directions is 10 N.
(c) The forces act at right angles to each other:
When two forces act at right angles to each other, we can find the net force using the Pythagorean theorem. The net force is equal to the square root of the sum of the squares of the magnitudes of the forces.
Net force = √(4 N)^2 + (14 N)^2
Net force = √16 + 196
Net force = √212 ≈ 14.6 N.
Therefore, the net force produced by the 4 N and 14 N forces acting at right angles to each other is approximately 14.6 N.