Answered

a rifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass of .992 kg that rests on a frictionless, horizontal surface and it attached to a coil spring. the impact compresses the spring 15.0 cm. calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.250 cm. find the magnitude of the block's velocity just after impact and the initial speed of the bullet.



Answer :

johanrusli

The magnitude of the block's velocity just after impact is about 2.60 m/s.

The initial speed of the bullet is about 325 m/s

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Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\large {\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Given:

mass of bullet = m₁ = 8.00 gram = 8 × 10⁻³ kg

mass of block = m₂ = 0.992 kg

initial speed of block = u₂ = 0 m/s

compression of spring = x = 15.0 cm = 0.15 m

spring constant = k = 0.750 ÷ (2.5 ×10⁻³) = 300 N/m

Asked:

final speed of block = v₂ = ?

initial speed of bullet = u₁ = ?

Solution:

Let:

final speed of the block just after impact = final speed of the bullet just after impact = v

Firstly , we will use Conservation of Energy as follows:

[tex]Ek = Ep[/tex]

[tex]\frac{1}{2}(m_1 + m_2)v^2 = \frac{1}{2} k x^2[/tex]

[tex](m_1 + m_2) v^2 = k x^2[/tex]

[tex](0.008 + 0.992) v^2 = 300 \times 0.15^2[/tex]

[tex]v^2 = 6.75[/tex]

[tex]v = \frac{3}{2}\sqrt{3} \texttt{ m/s}[/tex]

[tex]v \approx 2.60 \texttt{ m/s}[/tex]

The magnitude of the block's velocity just after impact is about 2.60 m/s

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Next , we will use Conservation of Momentum Law as follows:

[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]

[tex]0.008u_1 + 0.992(0) = 0.008(\frac{3}{2}\sqrt{3}) + 0.992(\frac{3}{2}\sqrt{3})[/tex]

[tex]0.008u_1 = \frac{3}{2}\sqrt{3}[/tex]

[tex]u_1 \approx 325 \texttt{ m/s}[/tex]

The initial speed of the bullet is about 325 m/s

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Learn more

  • Impacts of Gravity : https://brainly.com/question/5330244
  • Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
  • The Acceleration Due To Gravity : https://brainly.com/question/4189441
  • Newton's Law of Motion: https://brainly.com/question/10431582
  • Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

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