Physics, 11.01.2020 19:31 Ariellelyn176

A0.50-kg ball that is traveling at 6.0 m/s collides head-on with a 1.00-kg ball moving in the opposite direction at a speed of 12.0 m/s. the 0.50-kg ball bounces backward at 14 m/s after the collision. find the speed of the second ball after the collision.

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Answer from: jose477

-2 m/s

Explanation:

Assuming the collision is elastic, the total momentum must be conserved:

p_i = p_f

m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

where

m1 = 0.50 kg is the mass of the first ball

m2 = 1.00 kg is the mass of the second ball

u1 = +6.0 m/s is the initial velocity of the first ball

u2 = -12.0 m/s is the initial velocity of the second ball

v1 = -14 m/s is the final velocity of the first ball

v2 = ? is the final velocity of the second ball

By re-arranging the equation, we can find the final velocity of the 1.00 kg ball:

$v_2 = \frac{m_1 u_1 + m_2 u_2 - m_1 v_1}{m_2}=\frac{(0.50 kg)(6.0 m/s)+(1.00 kg)(-12 m/s)-(0.50 kg)(-14 m/s)}{1.00 kg}=-2 m/s$

which means, 2 m/s in the same direction the second ball was travelling before the collision.

Answer from: Quest

are there answer choices to this question? this seems like a question where you have options to choose from.

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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A0.50-kg ball that is traveling at 6.0 m/s collides head-on with a 1.00-kg ball moving in the opposi...