Question

An archer pulls the bowstring back for a distance of 0.470 m before releasing the arrow. The bow and string act like a spring whose spring constant is 425 N/m. a) What is the elastic potential energy of the drawn bow? b) The arrow has a mass of 0.0300 kg. How fast is it traveling when it leaves the bow?

Answer 1

Answer:

(a) 46.94 J.

(b)  55.95 m/s

Explanation:

(a)

Potential Energy: This is the energy of a body, due to its position. The S.I unit of potential energy is Joules (J).

The formula of potential energy in a stretched spring is

Ep = 1/2ke² .......................... Equation 1

Where Ep = potential energy of the spring, k = Force constant of the spring, e = extension or compression.

Given: k = 425 N/m, e = 0.47 m.

Substitute into equation 1

Ep = 1/2(425×0.47²)

Ep = 46.94 J.

(b)

at the instant When the arrow leaves the bow, the potential energy of the arrow is converted kinetic energy of the bow.

I.e,

Ep = 1/2mv² ............. Equation 2

Where m = mass of the arrow, v = velocity of the arrow.

make v the subject of the equation

v = √(2Ep/m)............. Equation 3

Given: Ep = 46.94 J, m = 0.03 Kg.

Substitute into equation 3

v = √(2×46.96/0.03)

v = √(93.92/0.03)

v = √(3130.67)

v = 55.95 m/s

Answer 2

Potential energy is the energy due to position. The potential energy of the given spring is 46.94 J

Potential Energy:

It is the energy of a body, due to the position of the different components. It is measured in Joules (J).

The formula of potential energy,

$U = \dfrac 12kx^2$

Where

$U$ = potential energy of the spring,

$k$ = Force constant of the spring = 425 N/m,

$x$ = extension or compression = 0.47 m.

Put the values in the equation,

$U =\dfrac 12(425\times 0.47^2)\\\\U= 46.94\rm \ J$

Therefore, the potential energy of the given spring is 46.94 J.

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