the ends of a light string are tied to two hooks A and Bin are ceiling which 100 cm apart horizontally,so that the length of string of string between hooks is 140 cm.A 650 g of mass is then attached by a second length of string to a point C on the first.80 cm from A,and hanged freely .Find by drawing or calculation ,the tensions in the portions AC and BC of the srting
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To find the tensions in the portions AC and BC of the string, we can first calculate the weight of the 650 g mass.
The weight of an object can be calculated using the formula:
Weight = Mass x Gravity
Given that the mass is 650 g (or 0.65 kg) and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight as:
Weight = 0.65 kg x 9.8 m/s^2 = 6.37 N
Now, let's proceed to the solution step by step:
1. Draw a diagram representing the situation described:
- Draw two hooks A and B, 100 cm apart, horizontally on a ceiling.
- Draw a horizontal line between the hooks representing the string.
- Label the length of the string between hooks as 140 cm.
- Label the point C on the string, 80 cm from A.
- Draw a vertical line from point C downward and label the weight of the 650 g mass as 6.37 N.
2. Now, we need to analyze the forces acting on point C:
- There are two tensions acting on point C, one in the portion AC and another in the portion BC.
- The weight of the 650 g mass acts vertically downward.
3. Calculate the tension in the portion AC:
- To calculate the tension in the portion AC, we need to consider the vertical forces acting on point C.
- The forces acting vertically on C are the tension in AC and the weight of the mass.
- Since point C is hanging freely, the vertical forces must be balanced (since there is no vertical acceleration).
- Therefore, the tension in AC is equal to the weight of the mass:
Tension AC = Weight of mass = 6.37 N
4. Calculate the tension in the portion BC:
- To calculate the tension in the portion BC, we need to consider the horizontal forces acting on point C.
- The forces acting horizontally on C are the tensions in AC and BC.
- Since point C is not accelerating horizontally, the horizontal forces must be balanced.
- Therefore, the tension in BC is equal to the tension in AC:
Tension BC = Tension AC = 6.37 N
So, the tensions in the portions AC and BC of the string are both 6.37 N.