a picture weighing 10 N is supported by two wires attached perpendicular to the picture. What is the tension force in each wire
10 N
0.2 N
20 N
5 N
The correct answer is 5 N.
When a picture is supported by two wires attached perpendicular to it, the tension force in each wire can be calculated by dividing the weight of the picture equally between the two wires.
Since the weight of the picture is 10 N, the tension force in each wire is 10 N / 2 = 5 N.
To calculate the tension force in each wire, we can use Newton's second law, which states that the sum of all the forces acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, since the picture is not accelerating, the sum of the forces acting on it is zero. Therefore, the tension forces in the wires must balance the weight of the picture.
Since there are two wires supporting the picture, the total tension force exerted by the wires must equal the weight of the picture, which is 10 N. Therefore, each wire shares an equal part of this total tension force.
So the tension force in each wire is 10 N ÷ 2 = 5 N.
Therefore, the tension force in each wire is 5 N.
To determine the tension force in each wire supporting the picture, we need to apply Newton's second law of motion, which states that the net forces acting on an object are equal to the mass of the object multiplied by its acceleration. In this case, since the picture is not moving vertically, the acceleration is zero. Therefore, the sum of the vertical forces must also be zero.
Let's assume the tension force in one of the wires is T1 and the tension force in the other wire is T2.
Since the picture weighs 10 N, we can say that the weight of the picture is equal to the sum of the tension forces in the wires:
T1 + T2 = 10 N
Since the wires are attached perpendicular to the picture, they are supporting the weight vertically. Therefore, the vertical component of each tension force must be equal to the weight of the picture.
Since we have two unknowns (T1 and T2), we need another equation to solve for their values. We can use the fact that the wires are attached perpendicular to the picture to apply the concept of vectors.
The tension forces in the wires and the weight of the picture form a right-angled triangle. The vertical component of the tension force in one wire is equal to the weight of the picture, and the horizontal component of both tension forces must balance each other out.
Let's calculate the vertical component of the tension force using trigonometry:
Vertical component = Weight of the picture = 10 N
Now, we can calculate the horizontal component of the tension force:
Horizontal component = Vertical component × tan(90°) = 10 N × tan(90°) = 0 N
Since the horizontal component of the tension force is zero, it means that both T1 and T2 must sum up to zero, with one tension force being negative (opposite direction) to balance out the other tension force.
Therefore, the tension force in each wire is:
T1 = -T2 = -5 N
Hence, the correct answer is 5 N (option D).