Consider the figure below.

www.webassign.net/sercp9/4-p-017-alt.gif
(a) Find the tension in each cable supporting the 688-N cat burglar. (Assume the angle θ of the inclined cable is 38.0°.)
inclined cable - ???
horizontal cable - ???
vertical cable - ???

the horizontal component of tensions must be the same, the upward force of the slanted cable must equal weight of man.

Tleft*sin38=weight, solve for Tleft
and Tleft*cos38=T right
vertical cable: mg

Well, well, well, it seems we have a cat burglar in the mix! Let's talk about the tension in those cables.

For the inclined cable, we have a tension force that is pulling upwards at an angle of 38.0°. Let's call this tension force "T incline". Now, remember that the cat burglar weighs 688 Newtons. So, the vertical component of the tension force should be equal to the weight of the burglar, meaning T incline * cos(38.0°) = 688 N. I trust your math skills to solve that equation!

Now, onto the horizontal cable. We'll call the tension force in this cable "T horizontal". Since this cable is horizontal (surprise, surprise), there is no vertical component to worry about. So, T horizontal = 688 N. Easy peasy!

Last but not least, we have the vertical cable. We'll call the tension force in this cable "T vertical". Again, there is no horizontal component to consider, so T vertical = 688 N. Not too shabby!

Remember, my friend, that the angle provided is crucial in determining the components of the tension forces. Happy calculating, and keep an eye out for any sneaky cat burglars!

To find the tension in each cable supporting the cat burglar, we need to resolve the weight of the cat burglar into its vertical and horizontal components.

Given:
Weight of the cat burglar (W) = 688 N
Angle of the inclined cable (θ) = 38.0°

Let's first find the vertical component of the weight. This is given by:

Vertical component of weight (Wv) = W * cos(θ)

Substituting the values, we get:

Wv = 688 N * cos(38.0°)
Wv ≈ 688 N * 0.788
Wv ≈ 542.144 N

Therefore, the tension in the vertical cable is approximately 542.144 N.

Now let's find the horizontal component of the weight. This is given by:

Horizontal component of weight (Wh) = W * sin(θ)

Substituting the values, we get:

Wh = 688 N * sin(38.0°)
Wh ≈ 688 N * 0.619
Wh ≈ 425.372 N

Therefore, the tension in the horizontal cable is approximately 425.372 N.

Finally, to find the tension in the inclined cable, we can use the Pythagorean theorem:

Tension in inclined cable = √(Tension in horizontal cable)^2 + (Tension in vertical cable)^2

Substituting the values, we get:

Tension in inclined cable = √(425.372 N)^2 + (542.144 N)^2
Tension in inclined cable ≈ √(180945.80 N^2 + 294257.51 N^2)
Tension in inclined cable ≈ √475203.31 N^2
Tension in inclined cable ≈ 689.23 N

Therefore, the tension in the inclined cable is approximately 689.23 N.

To find the tension in each cable supporting the cat burglar, we can use the principles of equilibrium. Let's analyze each cable separately:

1. Inclined cable:
The inclined cable makes an angle θ of 38.0° with the horizontal. Denote the tension in this cable as T_incl. Since the cat burglar is at rest, the vertical component of T_incl must balance the weight of the cat burglar, which is 688 N. Therefore, we have:

T_incl * sin(θ) = 688 N

2. Horizontal cable:
Denote the tension in the horizontal cable as T_horiz. Since the cat burglar is at rest, the horizontal component of T_incl must balance T_horiz. Thus, we have:

T_incl * cos(θ) = T_horiz

3. Vertical cable:
Denote the tension in the vertical cable as T_vert. Since the cat burglar is at rest, T_vert must be equal to the vertical component of T_incl, which is T_incl * sin(θ):

T_vert = T_incl * sin(θ)

To find the tensions in each cable, we need to solve this system of equations simultaneously. Here's how you can do it:

1. Plug in the value of θ (38.0°) into the equations for T_incl and T_vert:
T_incl * sin(38.0°) = 688 N (Equation 1)
T_vert = T_incl * sin(38.0°) (Equation 2)

2. Divide Equation 1 by sin(38.0°) to isolate T_incl:
T_incl = 688 N / sin(38.0°)

3. Substitute the value of T_incl in Equation 2 to find T_vert:
T_vert = (688 N / sin(38.0°)) * sin(38.0°)

4. Use the value of T_vert to find T_horiz:
T_horiz = T_incl * cos(38.0°)

By solving these equations using a calculator, you can find the values of T_incl, T_horiz, and T_vert, which represent the tension in each cable.