Question

A bow is launching an arrow. The extension of the thread before launch is 20 cm and the elastic constant is 50 N/m. The mass of the arrow is 20 g. The initial speed is zero. Find the speed when the extension was 10 cm?

Answer 1

To find the speed when the extension is 10 cm, we can use the principle of conservation of mechanical energy. We can substitute the given values into the equation, solve for the speed, and find that the speed is approximately 158.11 cm/s.

Step-by-step explanation:

To find the speed when the extension is 10 cm, we can use the principle of conservation of mechanical energy. The initial energy of the system is stored in the spring and is given by the equation:

1/2 k x^2 = 1/2 mv^2

where k is the elastic constant, x is the extension of the thread, m is the mass of the arrow, and v is the final speed.

Given that the initial extension is 20 cm and the elastic constant is 50 N/m, we can substitute the values into the equation:

1/2 (50) (0.20)^2 = 1/2 (0.020) v^2

Simplifying the equation:

5 = 0.0002 v^2

Dividing both sides by 0.0002:

v^2 = 25000

Taking the square root of both sides:

v = 158.11 cm/s

Therefore, the speed when the extension is 10 cm is approximately 158.11 cm/s.