A 10kg mass is suspended as shown:
i.gyazo[dotcom]/47dc49d5ec1eebe950472dba5f692e70.png
(remove the brackets)
What is the tension in the cord between points A and B? What is the tension in all of the cords?
Thanks for the help, I just can't figure it out...
figure at
http://i.gyazo.com/47dc49d5ec1eebe950472dba5f692e70.png
I will only do the right half (symmetry)
5 kg down on the right half
5 kg * 9.81 = 49 Newtons
so
tension below B: call it TL
TL cos 30 = 49
so
TL = 56.6 N
so component of TL to the left at B
TL left = 56.6sin 30 = 29.3 left
now the upper tension
call it TU
TU cos 45 = 49
so
TU = 69.3 N
so component of TU right at B
TUright = 69.3 sin 45 = 49 of course
NOW we have it
T + TL left = TU right = 49
T = 49 - 29.3
T = 19.7 Newtons
Thank you so much
To find the tension in the cord between points A and B, we need to consider the forces acting on the mass.
Let's assume the tension in the cord between points A and B is T_AB. The weight of the mass, acting vertically downwards, can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 10 kg × 9.8 m/s^2 (acceleration due to gravity)
Weight = 98 N
Since the mass is at rest, the net force acting on it is zero. Therefore, the tension in the cord between points A and B must be equal to the weight of the mass:
T_AB = Weight = 98 N
Now, let's consider the tension in all the cords. Since the mass is in equilibrium, the tension in the cord between point A and the ceiling and the tension in the cord between point B and the wall must balance the weight of the mass.
Let's assume the tension in the cord between point A and the ceiling is T_AC and the tension in the cord between point B and the wall is T_BC.
Since there is no vertical acceleration, the vertical components of the tensions must equal the weight of the mass:
T_AC cos(30°) + T_BC cos(45°) = Weight
T_AC cos(30°) + T_BC cos(45°) = 98 N
To find the values of T_AC and T_BC, we need to know the angles at which the cords are hanging. Could you please provide the angles or clarify the given angles in the diagram?
To determine the tension in the cord between points A and B, we need to consider the forces acting on the mass. In this case, the mass is in equilibrium, so the upward force (tension) in the cord must be equal to the downward force of gravity.
1. Calculate the force of gravity acting on the mass:
The force of gravity can be calculated using the formula F = m * g, where:
- F is the force of gravity
- m is the mass of the object (in this case, 10 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting these values, we have F = 10 kg * 9.8 m/s^2 = 98 N.
2. Determine the tension in the cord between A and B:
Since the mass is in equilibrium, the tension in the cord between A and B must be equal to the force of gravity acting on the mass. Therefore, the tension in the cord between A and B is 98 N.
3. Calculate the total tension in the cords:
To find the total tension in all the cords, we need to consider the forces acting on the mass. In addition to the force of gravity pulling it downwards, the mass is also being supported by another cord connected to point C.
Since the system is in equilibrium, the total upward forces must balance the total downward forces. We can assume the tension in the cord connected to point C is T_c and the tension in the cord between A and B is T_ab.
Using the equilibrium condition:
T_c + T_ab = F (the force of gravity on the mass)
Since we already know the force of gravity is 98 N (as calculated earlier), we can substitute that value into the equation and rearrange it to solve for T_c:
T_c = 98 N - T_ab
Therefore, the total tension in all the cords is equal to the sum of T_ab and T_c, which can be expressed as:
Total tension = T_ab + T_c = T_ab + (98 N - T_ab) = 98 N
Hence, the tension in all the cords is 98 N.