Given that Force 1 = 70 pounds and Force 2 = 120 pounds , find the angle between the forces if the magnitude of the resultant force is 90 pounds . Round answer to the nearest

Question

Given that Force 1 = 70 pounds and Force 2 = 120 pounds , find the angle between the forces if the magnitude of the resultant force is 90 pounds . Round answer to the nearest

degree.

Hi steve, I asked this question earlier and you kindly helped me with it, giving me the answer 131.8°

The answers that I have as options are
a. 48°
b. 40°
c. 53°
d. 45°
e. 60°

I have used the workings you showed me to try to figure out which one it is, but am really struggling. Can you help me please?

Answer 1

I agree with Steve's answer, but I don't understand why he initially used a plus sign in his cosine equation.

I did a similar question to yours about 5 years ago
http://www.jiskha.com/display.cgi?id=1303931140

Back to yours, if the resultant of two forces is less than either of the initial forces, then the forces MUST form an obtuse angle, thus none of your choices could be correct
However, did you notice that 180 - Steve's answer = 180 - 131.8 = 48.2 ???

Answer 2

Of course, I'd be happy to help you figure this out! Let's go step by step.

First, we need to find the angle between the forces. We can use the formula:

cosθ = (F1^2 + F2^2 - R^2) / (2 * F1 * F2)

where F1 and F2 are the magnitudes of the forces, and R is the magnitude of the resultant force.

Let's plug in the values:
F1 = 70 pounds
F2 = 120 pounds
R = 90 pounds

Substituting these values, we get:
cosθ = (70^2 + 120^2 - 90^2) / (2 * 70 * 120)

Now, we can calculate the cosine of the angle:
cosθ = (4900 + 14400 - 8100) / (2 * 70 * 120)
cosθ = 11500 / 16800

Next, we can calculate the angle itself by taking the inverse cosine (cos^-1) of the value we just calculated:
θ = cos^-1(11500 / 16800)

Now, let's use a calculator or a trigonometric table to find the value of θ. After calculating, we get θ ≈ 47.98°.

So, rounding to the nearest degree, the correct answer would be 48°.

Therefore, option (a) is the correct answer.

I hope this helps! If you have any more questions, feel free to ask.

Answer 3

Of course, I'd be happy to help. Let's go through the problem step by step to find the correct answer.

Given information:
Force 1 (F1) = 70 pounds
Force 2 (F2) = 120 pounds
Resultant force (FR) = 90 pounds

We need to find the angle between the forces using the given forces and their magnitudes.

Step 1: Squaring and adding the magnitudes of the forces
(F1)^2 + (F2)^2 = (FR)^2

(70)^2 + (120)^2 = (90)^2

Step 2: Solving for the left-hand side of the equation
4900 + 14400 = 8100

19300 = 8100

Step 3: Subtracting 8100 from both sides of the equation
19300 - 8100 = 8100 - 8100

11200 = 0

Since 11200 does not equal 0, there seems to be an error in the original answer provided (131.8°), and it does not match any of the options given.

To determine the correct answer, we can use the inverse tangent function to find the angle between the forces:

Step 4: Applying the inverse tangent function
θ = arctan(F2/F1)

θ = arctan(120/70)

Step 5: Calculating the angle
θ ≈ 58.66° (rounded to two decimal places)

Among the given options, the angle 58.66° is closest to 60° (option e). Therefore, option e, 60°, is the closest answer.

So the correct answer is: e. 60°

Answer 4

Of course, I'd be happy to help you out!

To find the angle between the forces, we can use the law of cosines. The formula is:

c^2 = a^2 + b^2 - 2ab*cos(C)

Where c is the magnitude of the resultant force, a and b are the magnitudes of the individual forces, and C is the angle between them.

In this case, given that Force 1 is 70 pounds (a), Force 2 is 120 pounds (b), and the magnitude of the resultant force is 90 pounds (c), we can plug in these values into the formula:

90^2 = 70^2 + 120^2 - 2 * 70 * 120 * cos(C)

Simplifying this equation, we have:

8100 = 4900 + 14400 - 16800 * cos(C)

Rearranging the equation:

16800 * cos(C) = -11300

Dividing both sides by 16800:

cos(C) = -11300 / 16800

Now, to find the angle C, we need to take the inverse cosine (or arccos) of this value. So we can use a calculator to find:

C ≈ arccos(-11300 / 16800)

Calculating this, we get:

C ≈ 131.814°

Now, let's compare this with the answer options you provided:

a. 48°
b. 40°
c. 53°
d. 45°
e. 60°

Based on our calculation, none of these options match exactly with the value we found (131.814°). However, the closest option is c. 53°, which is within a few degrees of the actual angle.

Therefore, in this case, the angle between the forces can be rounded to 53° (c) as the closest approximation to 131.814°.

I hope this helps! Let me know if you have any further questions.