An archer must exert a force of 445 N on the bowstring shown in Figure (a) such that the string makes an angle of è = 34.0° with the vertical.

(a) Determine the tension in the bowstring.
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My answer was 420.525, but it is within 10% of the correct value.

I used Newton's 2nd Law and derived @:

T=445/2sin(34)

***Please help! What am I doing wrong?

Your formula is correct but should yield 398 N for the tension. You made a computational error somewhere.

Also, it is simply a statement of force equilibrium, not Newton's second law. Finally, it has nothing to do with Waves, as your subject title implies.

Yes, 2 T sin 34 = F = 445

T = 445 /(2 sin 34)
T = 398 N

Your calculator does not agree with mine.

Thank you so much!

To find the tension in the bowstring, you need to consider the forces acting on the bowstring. In this case, there are two forces: the tension force exerted by the archer on the bowstring and the vertical component of the weight of the bowstring.

Let's break down the forces acting on the bowstring:

1. Tension Force: This is the force exerted by the archer on the bowstring and is directed along the string. We need to calculate this force.

2. Weight of the Bowstring: This is the force due to gravity acting on the bowstring and is directed downwards. The weight can be broken down into two components: the vertical component and the horizontal component. The vertical component is what is relevant for this problem.

To determine the tension in the bowstring, we need to consider the vertical equilibrium of forces. The vertical force on the bowstring is the sum of the vertical components of tension and weight. Since the bowstring is in equilibrium (not accelerating vertically), these forces must balance each other.

The vertical component of the weight of the bowstring can be found using trigonometry. It is given by:

Weight Vertical = Weight × sin(θ)

where Weight is the magnitude of the weight and θ is the angle made by the bowstring with the vertical (given as è = 34.0°).

Now, we can set up the equation for vertical equilibrium:

Tension + Weight Vertical = 0

Substituting the values, we get:

Tension + Weight × sin(θ) = 0

Solving for the tension (T), we have:

Tension = -Weight × sin(θ)

Since weight is a positive quantity, the negative sign ensures that the tension is in the opposite direction to the weight direction.

Now, we need to find the weight of the bowstring. Weight is given by the equation:

Weight = mass × acceleration due to gravity

Since the mass of the bowstring is not given, we can use the relationship between weight, mass, and acceleration due to gravity:

Weight = mass × acceleration due to gravity

Now, substituting the values, we have:

Weight = 445 N / (acceleration due to gravity)

The acceleration due to gravity is approximately 9.8 m/s².

Once you have the weight, substitute it into the equation for tension:

Tension = -(Weight × sin(θ))

Now, calculate the tension using this equation:

Tension = -(Weight × sin(θ))

Tension = -(445 N / (9.8 m/s²)) × sin(34.0°)

This should give you the correct value for the tension in the bowstring.