Respuesta :
Answer:
c. 8.67 cm/s
Explanation:
From the law of conservation of momentum,
Total momentum before the thread was burned = Total momentum after was burned
mu + m'u' = mv + m'v'...................... Equation
Where m = mass of the heavier cart, m' = mass of the lighter cart, u = initial velocity of the bigger cart, u' = initial velocity of the smaller cart, v = final velocity of the bigger cart, v' = final velocity of the smaller cart.
Note: Both cart where momentarily at rest, as such u = u' = 0. i.e the total momentum before the thread was burn = 0
And assuming the left is positive,
We can rewrite equation 1 as
mv + m'v' = 0............................................ Equation 2
Given: m = 4.5 kg, m' = 1.5 kg, v' = 26 cm/s
Substitute into equation 2,
4.5v + 1.5(26) = 0
4.5v + 39 = 0
4.5v = -39
v = -39/4.5
v = -8.67 cm/s.
Note: v is negative because it moves to right.
Hence the velocity of the 4.5 kg cart = 8.67 cm/s.
The right option is c. 8.67 cm/s
The velocity of the cart which has 4.5 kg of mass is 8.67 cm/s. Option C is correct.
From the law of conservation of momentum,
[tex]mu + m'u' = mv + m'v'[/tex]
Where
[tex]m[/tex] = mass of the heavier cart = 4.5 kg
[tex]m'[/tex] = mass of the lighter cart = 1.5 kg,
[tex]u[/tex]= initial velocity of the bigger cart,
[tex]u'[/tex] = initial velocity of the smaller cart,
[tex]v[/tex] = final velocity of the bigger cart,
[tex]v'[/tex] = final velocity of the smaller cart = 26 cm/s
Since the carts were momentarily at the rest, the total momentum before the thread was burned is zero.
So,
[tex]mv + m'v' = 0[/tex]
Put the values in the formula,
[tex]4.5v + 1.5(26) = 0\\\\v =\dfrac { -39}{4.5}\\\\\v = -8.67 \rm \ cm/s.[/tex]
Therefore, the velocity of the cart which has 4.5 kg of mass is 8.67 cm/s.
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