contestada

A sledge hammer has a mass of 4.0 kg and is moving at a speed of 6.0m/s when it strikes a fence post, driving it 10 cm further into the ground.
A) what was the kinetic energy of the sledge hammer?
B) what is the average force exerted on the fence post by the hammer?

Respuesta :

Part a)

kinetic energy of the hammer will be

[tex]KE = \frac{1}{2} mv^2[/tex]

here we know that

m = 4 kg

v = 6 m/s

now by the equation of kinetic energy we have

[tex]KE = \frac{1}{2}*4 * 6*6[/tex]

[tex]KE = 72 J[/tex]

Part b)

for finding the force we will have

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

here we know that

[tex]v_f = 0[/tex]

[tex]v_i = 6 m/s[/tex]

[tex]d = 10 cm = 0.10 m[/tex]

now from above equation we have

[tex]0 - 6^2 = 2 * a * 0.10[/tex]

[tex]a = -180 m/s^2[/tex]

now by Newton's II law we have

[tex]F = ma[/tex]

[tex]F = 4*180 = 720 N[/tex]

so it requires 720 N.

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