A mass of 15kg is supsended by 2 cords from a ceiling. the cords have lenghts of 15cm and 20cm, and the distance between the points wheere they are attached on the ceiling ia 25cm. determine the tension in each of the 2 cords.
can someone please tell me the steps to take inorder to solve this question. Thanks in advance:)
If anyone is lost with the Reiny's answers, you just convert the kilo answers to newtons. m*g = kg*9.81m/s^2 kinda thing
To determine the tension in each of the two cords, you can break down the problem into two components: the vertical component and the horizontal component. Here are the steps to solve the problem:
Step 1: Draw a diagram: Sketch the situation described in the problem, indicating the mass, the two cords, and the attachment points on the ceiling.
Step 2: Break down the problem into vertical and horizontal components: Since the mass is in equilibrium, the vertical component of the tensions in the cords must equal the weight of the mass, and the horizontal component should cancel each other out.
Step 3: Use trigonometry to find the vertical component of the tension: Consider one of the cords (either one) and label the angle formed between the cord and the vertical line as θ1. The vertical component of the tension in the cord can be calculated as T1 * cos(θ1), where T1 is the tension in that cord. Use the length of the cord and the given distance between the attachment points on the ceiling for trigonometric calculations.
Step 4: Use trigonometry to find the horizontal component of the tension: The horizontal component of the tension in one cord can be calculated as T1 * sin(θ1).
Step 5: Apply the principle of equilibrium: Since the mass is in equilibrium, the vertical components of the tensions in both cords should add up to counterbalance the weight of the mass. Therefore, you can write an equation: T1 * cos(θ1) + T2 * cos(θ2) = mg; here, m is the mass and g is the acceleration due to gravity.
Step 6: Apply the principle of zero horizontal acceleration: Since the horizontal components of the tensions in both cords should cancel each other out, you can write another equation: T1 * sin(θ1) = T2 * sin(θ2).
Step 7: Solve the system of equations: You now have two equations with two unknowns (T1 and T2). Use the given values and trigonometric functions to solve for the tensions in the cords.
Step 8: Substitute the calculated values into the equations and solve: Replace the trigonometric functions and simplify the equations, then solve for T1 and T2.
Step 9: Check your solution: Verify that the tensions you calculated satisfy the conditions of equilibrium and make physical sense.
By following these steps, you should be able to determine the tension in each of the two cords.
To solve this question, you can use the principles of equilibrium. Here are the steps you can follow:
1. Draw a diagram: Start by drawing a labeled diagram representing the given information. Draw a dot to represent the mass, and label the two cords as cord A (15 cm) and cord B (20 cm). Label the distance between the points where cords A and B are attached on the ceiling as 25 cm.
2. Identify the forces: Identify the forces acting on the mass. In this case, you have the weight of the mass acting downward, and the tensions in cords A and B acting upward.
3. Apply Newton's first law: According to Newton's first law, an object is in equilibrium when the net force acting on it is zero. In this case, since the mass is not accelerating, the sum of the upward forces (tension in cord A and tension in cord B) must equal the downward force (weight of the mass).
4. Resolve forces: Resolve the forces along the two cords. Since the cords are at different angles, you need to take into account the components of the tensions in the vertical direction.
5. Apply trigonometry: Use trigonometry to find the components of the tensions in the vertical direction. The components of the tensions can be found using the sine function, with the angles formed between the cords and the vertical direction.
6. Write the equilibrium equation: Write an equation based on the equilibrium condition. The sum of the upward forces (tension in cord A and tension in cord B) must equal the downward force (weight of the mass).
7. Solve the equation: Use the equation to solve for the tensions in cords A and B. Substitute the values you have found into the equation and solve for the tensions.
By following these steps, you should be able to determine the tension in each of the two cords.
Draw a position diagram showing the cords
by cosine law, find the angle between the 25 and 20 cm cords
15^2 = 25^2 + 20^2 - 2(25)(20)cosß
ß = 36.87º
AHHH, just realized our triangle is right-angled since 25^2 = 15^2+20^2
so the other angle is 53.13º , lucky.
Now draw a vector diagram with a vertical line to represent the 15 kg,
from the top of that vertical line draw a line parallel to the 15 cm cord, and from the bottom of the vertical line, draw a line parallel to the 20 cm cord until they meet.
This should also be a right-angled triangle with the top angle 53.13, and the bottom angle 36.87 and 15 as the hypotenuse
Let T1 be the tension in the 15 cm cord and T2 the tension in the 20 cm cord
cos 53.13 = T1/15
T1 = 9 kg
and in the same way
T2 = 15 cos 36.87 = 12 kg