Physics, 19.12.2019 08:31, FlayMaster101

A2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. if the collision is perfectly elastic, what is the final speed of the 2.3-kg object?

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answered: patricialovett4570

The final speed of the 2.3-kg object is about 7.1 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.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Given:

mass of object 1 = m₁ = 2.3 kg

initial velocity of object 1 = u₁ = 6.1 m/s

mass of object 2 = m₂ = 3.5 kg

initial velocity of object 2 = u₂ = -4.8 m/s

Asked:

final velocity of object 1 = v₁ = ?

Solution:

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

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

2.3(6.1) + 3.5(-4.8) = 2.3v_1 + 3.5v_2

-2.77 = 2.3v_1 + 3.5v_2 → Equation 1

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If the collision is perfectly elastic , then:

u_1 - u_2 = v_2 - v_1

6.1 - (-4.8) = v_2 - v_1

10.9 = v_2 - v_1 → Equation 2

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Let's solve the two Equations above:

(Equation 1) - 3.5(Equation 2) ↓

-2.77 - 3.5(10.9) = 2.3v_1 + 3.5v_2 - 3.5(v_2 - v_1)

(-2.77) - 3.5(10.9) = (2.3v_1 + 3.5v_2) - 3.5(v_2 - v_1)

-40.92 = 5.8v_1

$v_1 = -40.92 \div 5.8$

$v_1 \approx -7.1 \texttt{ m/s}$

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Learn moreImpacts of Gravity : Effect of Earth’s Gravity on Objects : The Acceleration Due To Gravity : Newton's Law of Motion: Example of Newton's Law:

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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

A2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite

answered: Guest

magnityde and direction

answered: Guest

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.