Consider the 608 N weight held by two cables shown below. The left-hand cable had ten- sion T2 and makes an angle of 44◦ with the ceiling. The right-hand cable had tension T1 and makes an angle of 42◦ with the ceiling.

a) What is the tension in the cable labeled T1 slanted at an angle of 42◦?
Answer in units of N.
(part 2 of 2) 10.0 points
a) What is the tension in the cable labeled T2 slanted at an angle of 44◦?
Answer in units of N.

a. -T2*Cos44 + T1*Cos42 = 0.

T1*Cos42 = T2*Cos44.
T2 = 1.033T1.

T2*sin44 + T1*sin42 = -(-608) = 608 N.
1.033T1*sin44 + T1*sin42 = 608.
0.718T1 + 0.669T1 = 608.
1.39T1 = 608.
T1 = 438.3 N.

b. T2 = 1.033 * 438.3 = 452.8 N.

A: Well, tension is like a stressful relationship, always pulling things apart. Now, let's calculate the tension in the first cable, T1.

We have an angle of 42 degrees and a weight of 608 N. So, let's call the tension in cable T1 "T1."

Using some trigonometry magic, we can say that:

sin(42 degrees) = T1 / 608 N

Now, let's solve for T1:

T1 = 608 N * sin(42 degrees)

Calculating this out, we get:

T1 ≈ 400.28 N

So, the tension in the cable labeled T1 slanted at an angle of 42 degrees is approximately 400.28 N.

Now, let's move on to the second cable, T2. This one has an angle of 44 degrees, so let's call the tension in cable T2 "T2."

Using the same trick as before, we can say:

sin(44 degrees) = T2 / 608 N

Now, let's solve for T2:

T2 = 608 N * sin(44 degrees)

Calculating this out, we get:

T2 ≈ 420.60 N

So, the tension in the cable labeled T2 slanted at an angle of 44 degrees is approximately 420.60 N.

Remember, these calculations assume that the cables are perfectly supporting the weight and not getting tangled up in any knots. It's like a circus balancing act!

To find the tension in the cable labeled T1 slanted at an angle of 42°, we can use trigonometry. The vertical component of T1 is equal to the weight being held, which is 608 N. Since the cable makes an angle of 42° with the ceiling, the vertical component can be found using the sine function: sin(42°) = vertical component / T1. We can rearrange this equation to solve for the tension T1: T1 = vertical component / sin(42°).

Let's calculate the value of T1:

T1 = 608 N / sin(42°)
= 608 N / 0.6691
≈ 909.267 N

Therefore, the tension in the cable labeled T1 slanted at an angle of 42° is approximately 909.267 N.

Now, let's move on to find the tension in the cable labeled T2 slanted at an angle of 44°. Similar to the previous case, the vertical component of T2 is equal to 608 N, and the cable makes an angle of 44° with the ceiling. Using the same logic, we can calculate T2 using the sine function: T2 = vertical component / sin(44°).

Let's calculate the value of T2:

T2 = 608 N / sin(44°)
= 608 N / 0.6947
≈ 875.076 N

Therefore, the tension in the cable labeled T2 slanted at an angle of 44° is approximately 875.076 N.

To find the tension in the cable labeled T1 slanted at an angle of 42°, we can use the concept of static equilibrium. Static equilibrium means that the sum of the forces acting on an object is zero.

Let's label the angles and forces on the free body diagram. The weight of 608 N is acting downward. The tension in the cable labeled T1 is acting upward at an angle of 42° with the ceiling.

Since the weight is in equilibrium, we can set up the equation: ΣFy = 0, where ΣFy is the sum of the vertical forces.

The vertical component of the tension in cable T1 can be calculated as: T1 * sin(42°). This vertical component of T1 should balance the weight of 608 N.

So, we have the equation: T1 * sin(42°) = 608 N.

Now, we can solve for T1 by dividing both sides of the equation by sin(42°):

T1 = 608 N / sin(42°).

Calculating this expression will give us the value of tension T1 in Newtons.

To find the tension in the cable labeled T2 slanted at an angle of 44°, we can use a similar approach.

Using the concept of static equilibrium, we can set up the equation: ΣFy = 0.

The vertical component of the tension in cable T2 can be calculated as: T2 * sin(44°). This vertical component of T2 should again balance the weight of 608 N.

Therefore, we have the equation: T2 * sin(44°) = 608 N.

Now, we can solve for T2 by dividing both sides of the equation by sin(44°):

T2 = 608 N / sin(44°).

Calculating this expression will give us the value of tension T2 in Newtons.

Remember to use a calculator to find the values of sin(42°) and sin(44°) before performing the calculations.