Physics, 09.12.2020 08:00 baileysosmart

On an air track, a 4-kg cart moving at 3 m/s collides with a 2-kg cart that is initially at rest. If the two carts stick together, what will be their velocity
after the collision? Show all calculations, including any equation(s) used,
and include correct measurement units. *
Your answer

Answers: 2

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Answer from: hockeystar0033

v₃ = 2 [m/s]

Explanation:

To solve such problems we must use the principle of conservation of momentum. That is, the linear momentum is conserved before and after the collision.

P = m*v

where:

P = linear momentum [kg*m/s]

m = mass [kg]

v = velocity [m/s]

The momentum is conserved before and after the collision, in this way we can obtain the following equation.

$(m_{1}*v_{1})+(m_{2}*v_{2})=(m_{1}+m_{2})*v_{3}$

where:

m₁ = mass of the cart moving = 4 [kg]

v₁ = velocity of the cart moving before the collision = 3 [m/s]

m₂ = mass of the cart initially at rest = 2 [kg]

v₂ = velocity of the cart at rest = 0

v₃ = velocity of the two carts combined (carts stick together) after the collision [m/s]

$(4*3)+(2*0)=(4+2)*v_{3}\\v_{3}=12/6\\v_{3}=2[m/s]$

Answer from: Quest

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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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