Anonymous
Anonymous asked in Science & MathematicsPhysics · 7 years ago

Tough Physics Question - Grade 12 - Kinematics/Forces/Energy all in one - Please show steps?

A bullet with a mass of 45 g is fired into a 8.3 kg block of wood resting on a floor against a spring (the coefficient of kinetic friction between the floor and the block is 0.24). This idea spring (k=76 N/m) has a maximum compression of 28 cm. What was the initial speed of the bullet?

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  • Jim
    Lv 7
    7 years ago
    Favorite Answer

    This question involves application of the two conservation principles:

    Conservation of Momentum is applicable when bullet collides into wood block.

    Conservation of Energy is applicable when block/bullet compress (ideal) spring.

    Since the question asks for the initial speed of bullet let that unknown = v

    and

    Let the speed of block/bullet combination = V

    The momentum of block/bullet combination = (0.045 + 8.3)V = 8.345V

    The KE of block/bullet combination = 1/2(8.345)V² = 4.1725V²

    SPE = 1/2kx² = (0.5)(76)(0.28)² = 2.9792 J

    by conservation of energy => 2.9792 = 4.1725V²

    V² = 0.714008388

    V = 0.84499 m/s

    The momentum of block/bullet combination = (8.345)(0.84499) = 7.05144 kgm/s

    The momentum of bullet prior to hitting block = mv = 0.045v

    by conservation of momentum => 0.045v = 7.05144

    v = 7.05144/0.045 = 157 m/s ANS

  • Whome
    Lv 7
    7 years ago

    To find the initial velocity of the bullet and block after impact we apply conservation of energy principles

    The maximum spring potential plus the energy lost to friction will equal the initial kinetic energy

    KE = PS + U

    ½mv² = ½kx² + Fd

    as the spring is resting against the block before impact, then d = x

    F will be the friction force or

    F = μmg

    ½mv² = ½kx² + μmgx

    v² = kx²/m + 2μgx

    v = √(kx²/m + 2μgx)

    v = √(76(0.28²) / (8.3 + 0.045) + 2(0.24)9.81(0.28))

    v = 2.032 m/s

    Now we use conservation of momentum to find the initial bullet velocity

    mu1 + Mu2 = (m + M)v

    as the block initial velocity, u2, is zero

    u1 = (m + M)v / m

    u1 = (0.045 + 8.3)2.032 / 0.045

    u1 = 377 m/s

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