Two people pull on a stubborn mule. The first person makes an angle of 15 degrees with respect to the horizontal and the second person 30 degrees with respect to the horizontal. If the first person applies a force of 80N and the second 120N, how much force would they be exerting on the mule?
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To find the total force exerted on the mule, we need to determine the horizontal components of the forces applied by each person and then add them together.
Let's start by finding the horizontal component of the force exerted by the first person. We'll use trigonometry to do this. The horizontal component (F1x) can be calculated using the formula:
F1x = F1 * cos(angle1)
where F1 is the force applied by the first person (80N) and angle1 is the angle made by the first person with respect to the horizontal (15 degrees).
F1x = 80N * cos(15 degrees)
Using a scientific calculator, we can evaluate cos(15 degrees) ≈ 0.9659.
F1x = 80N * 0.9659 ≈ 77.27N
Now let's find the horizontal component of the force exerted by the second person. Similar to before, the horizontal component (F2x) can be calculated using the formula:
F2x = F2 * cos(angle2)
where F2 is the force applied by the second person (120N) and angle2 is the angle made by the second person with respect to the horizontal (30 degrees).
F2x = 120N * cos(30 degrees)
Using a scientific calculator, we can evaluate cos(30 degrees) ≈ 0.8660.
F2x = 120N * 0.8660 ≈ 103.92N
Now we can add the horizontal components of the forces applied by each person to find the total force exerted on the mule:
Total force = F1x + F2x
= 77.27N + 103.92N
≈ 181.19N
Therefore, the total force exerted on the mule is approximately 181.19 Newtons.