Two artifacts in a museum display are hung from vertical walls by very light wires. Wire T1 is horizontal from the left wall and goes to a center weight of 177N and wire T2 is at a 53 degree angle with the right wall heading from right to left downwards towards the center weight of 177N. From the center weight a wire T3 hangs vertically to a 40kg object.
Find the tension on T1, T2 and T3.
T3 solved but don't know how to calc. T1 and T2.
Got an answer and that is much appreciated but I don't think that it applied properly to my question.
Look up this question on google and you can get a diagram that may better help someone explain how to get T1 horizontal tension and T2 incline tension.
Still need the help please.
To find the tensions in wires T1 and T2, we can use the principles of static equilibrium. In this case, the sum of the forces in both the horizontal and vertical directions must be equal to zero.
Let's break down the problem step by step:
1. Tension in T3:
Given that the weight hanging from T3 is 40 kg, we can calculate the force acting on it using the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity. Since g is approximately 9.8 m/s², the force on T3 is 40 kg * 9.8 m/s² = 392 N.
2. Tension in T1:
Since wire T1 is horizontal, the tension force in T1 will have no vertical component. Therefore, the tension force in T1 will be equal to the weight hanging from it, which is the 177 N center weight. Thus, the tension in T1 is also 177 N.
3. Tension in T2:
To find the tension in T2, we need to consider the forces acting on it. These forces include the vertical component of the tension in T2 and the weight of the center weight.
First, we need to find the vertical component of the tension in T2. We can do this by multiplying the tension in T2 by the sine of the angle it makes with the vertical direction. Given that the angle is 53 degrees, we can calculate the vertical component of T2 as follows:
Vertical component of T2 = T2 * sin(53°)
Next, we need to consider the weight of the 177 N center weight, which acts downward. The weight of an object can be calculated using the same equation as earlier: F = m * g = 177 N.
Since the vertical forces are in equilibrium, the vertical component of T2 must balance the weight of the center weight.
Therefore:
Vertical component of T2 = 177 N
Now that we have the vertical component of T2, we can find the tension in T2 itself. Recall that the tension force in T2 also has a horizontal component, which balances out the horizontal tension force in T1. As a result, the horizontal component of T2 will be equal to the horizontal tension force in T1, which is 177 N.
Since T2 is at an angle of 53 degrees with the vertical, we can find the horizontal component as follows:
Horizontal component of T2 = T2 * cos(53°)
Since the horizontal component is equal to 177 N, we can equate the two expressions and solve for T2:
Horizontal component of T2 = 177 N
T2 * cos(53°) = 177 N
Finally, we can find the tension in T2 by dividing the right-hand side of the equation by cos(53°):
T2 = 177 N / cos(53°)
Once you substitute the value of cos(53°) into the equation and perform the calculation, you will obtain the tension in T2.