Here is the exact problem and all the info... I only need help with part (*******B*****)
Problem A traffic light weighing 1.04 102 N hangs from a vertical cable tied to two other cables that are fastened to a support, as in Figure 4.12a. The upper cables make angles of ?1 = 39.0° and ?2 = 51.0° with the horizontal. Find the tension in each of the three cables.
Figure 4.12 (a) Traffic light suspended by cables. (b) A free-body diagram for the traffic light. (c) A free-body diagram for the knot joining the cables.
Strategy There are three unknowns, so we need to generate three equations relating them, which can then be solved. One equation can be obtained by applying Newton's second law to the traffic light, which has forces in the y-direction only. Two more equations can be obtained by applying the second law to the knot joining the cables -- one equation from the x-component and one equation from the y-component.
Solution
Find T3 from Figure 4.12b, using the condition of equilibrium.Fy = 0 T3 - Fg = 0
T3 = Fg = N
Using Figure 4.12c, resolve all three tension forces into components and construct a table for convenience.
Forcex-componenty-component
T1-T1 cos 39.0°T1 sin 39.0°
T2T2 cos 51.0°T2 sin 51.0°
T30-104 N
Apply the conditions for equilibrium to the knot, using the components in the table.
Fx = -T1 cos 39.0° + T2 cos 51.0° = 0(1)
Fy = T1 sin 39.0° + T2 sin 51.0° - T3 = 0(2)
There are two equations and two remaining unknowns. Solve equation (1) for T2.
Substitute the result for T2 into Equation (2).T1 sin 39.0° + (1.235 T1) (sin 51.0°) - 104 N = 0
T1 = N
T2 = (1.235)T1 = N
Remarks It's very easy to make sign errors in this kind of problem. One way to avoid them is to always measure the angle of a vector from the positive x-direction. The trigonometric functions of the angle will then automatically give the correct signs for the components. For example, 1 makes an angle of 180° - 39.0° = 141° with respect to the positive x-axis, and its x-component, T1 cos 141°, is negative, as it should be.
Exercise 4.5Hints: Getting Started | I'm Stuck
*****B) Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 86 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same.)
? = °
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.
Problem A traffic light weighing 1.04 102 N hangs from a vertical cable tied to two other cables that are fastened to a support, as in Figure 4.12a. The upper cables make angles of ?1 = 39.0° and ?2 = 51.0° with the horizontal. Find the tension in each of the three cables.
Figure 4.12 (a) Traffic light suspended by cables. (b) A free-body diagram for the traffic light. (c) A free-body diagram for the knot joining the cables.
Strategy There are three unknowns, so we need to generate three equations relating them, which can then be solved. One equation can be obtained by applying Newton's second law to the traffic light, which has forces in the y-direction only. Two more equations can be obtained by applying the second law to the knot joining the cables -- one equation from the x-component and one equation from the y-component.
Solution
Find T3 from Figure 4.12b, using the condition of equilibrium.Fy = 0 T3 - Fg = 0
T3 = Fg = N
Using Figure 4.12c, resolve all three tension forces into components and construct a table for convenience.
Forcex-componenty-component
T1-T1 cos 39.0°T1 sin 39.0°
T2T2 cos 51.0°T2 sin 51.0°
T30-104 N
Apply the conditions for equilibrium to the knot, using the components in the table.
Fx = -T1 cos 39.0° + T2 cos 51.0° = 0(1)
Fy = T1 sin 39.0° + T2 sin 51.0° - T3 = 0(2)
There are two equations and two remaining unknowns. Solve equation (1) for T2.
Substitute the result for T2 into Equation (2).T1 sin 39.0° + (1.235 T1) (sin 51.0°) - 104 N = 0
T1 = N
T2 = (1.235)T1 = N
Remarks It's very easy to make sign errors in this kind of problem. One way to avoid them is to always measure the angle of a vector from the positive x-direction. The trigonometric functions of the angle will then automatically give the correct signs for the components. For example, 1 makes an angle of 180° - 39.0° = 141° with respect to the positive x-axis, and its x-component, T1 cos 141°, is negative, as it should be.
Exercise 4.5Hints: Getting Started | I'm Stuck
*****B) Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 86 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same.)
? = °
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.