Two toy locomotives approach each other along the same line, and upon collision both stop dead still. One locomotive has three times the speed of the other and the sum of their masses is 4.48 kg.
What is the mass of the faster locomotive?
What is the mass of the faster locomotive?
Since they come to a dead stop, they had equal and opposite momenta beforer the collision
Let M1 be the mass of the faster toy locomotive (speed V1) and M2 be mass of the slow the slow one (with speed V1/3).
M2 = 4.48 - M1
M2*V1/3 = M1*V1 = (4.48 -M1)*V1/3
V1 cancels out.
M1 = (4.48 -M1)/3
(4/3)M1 = 1.4933 kg
M1 = 1.12 kg
M2 = 3.36 kg
Let's assume the mass of the slower locomotive is x kg.
According to the given information, the faster locomotive has three times the speed of the slower locomotive.
So, the speed of the slower locomotive is x m/s, and the speed of the faster locomotive is 3x m/s.
Now, let's consider the conservation of momentum. Momentum is defined as the product of mass and velocity.
The momentum of the slower locomotive before the collision is x kg * x m/s = x^2 kg*m/s.
The momentum of the faster locomotive before the collision is 3x kg * (3x m/s) = 9x^2 kg*m/s.
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
So, x^2 + 9x^2 = 4.48 kg*m/s
Combining like terms, we get 10x^2 = 4.48 kg*m/s.
Dividing both sides by 10, we get x^2 = 0.448 kg*m/s.
Taking the square root of both sides, we get x = 0.67 kg.
Therefore, the mass of the faster locomotive is 3x = 3 * 0.67 kg = 2.01 kg.
To find the mass of the faster locomotive, let's go step by step.
Let's denote the mass of the slower locomotive as "m" and the mass of the faster locomotive as "3m" (since it is three times as fast).
According to the question, the sum of their masses is 4.48 kg:
m + 3m = 4.48
Combining the like terms:
4m = 4.48
To find the value of "m," divide both sides of the equation by 4:
m = 4.48/4
Simplifying the right side:
m = 1.12
Therefore, the mass of the slower locomotive is 1.12 kg.
To find the mass of the faster locomotive, multiply the mass of the slower locomotive by 3:
3m = 3 * 1.12
Calculating:
3m = 3.36
Therefore, the mass of the faster locomotive is 3.36 kg.