Physics, 16.11.2019 06:31 Tuxkie

(25%) problem 3: a bullet is fired horizontally into an initially stationary block of wood suspended by a string and remains embedded in the block. the bullet’s mass is m = 0.0085 kg, while that of the block is m = 0.99 kg. after the collision the block/bullet system swings and reaches a maximum height of h = 0.95 m above its initial height. neglect air resistance.

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Answer from: arielpraczko1

The initial velocity of the bullet is 507.4 m/s

Your question is not complete, it seems to be missing the following information;

find the initial velocity of the bullet

The given parameters;

mass of the bullet, m₁ = 0.0085 kgmass of block, m₂ = 0.99 kgmaximum height attained by the system, h = 0.95 m

The final velocity of the system is calculated as;

$\frac{1}{2} (m_1 + m_2) v_{max}^2 = (m_1 + m_2) gh_{max}\\\\v_{max}^2 = 2gh_{max}\\\\v_{max} = \sqrt{2gh_{max}} \\\\v_{max} = \sqrt{2\times 9.8 \times 0.95} \\\\v_{max} = 4.32 \ m/s$

The initial velocity of the bullet is calculated by applying the principle of conservation of linear momentum;

$m_1 u_1 + m_2 u_2 = v(m_1 + m_2)\\\\0.0085u_1 + 0 = 4.32(0.0085 + 0.99)\\\\0.0085u_1 = 4.313\\\\u_1 = \frac{4.313}{0.0085} \\\\u_1 = 507.4 \ m/s$

Thus, the initial velocity of the bullet is 507.4 m/s

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Answer from: Quest

f is prop to m1xm2 double m1 double force

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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(25%) problem 3: a bullet is fired horizontally into an initially stationary block of wood suspende...