A force of 5N gives a mass M,an acceleration of 18ms-2qnd a mass m,an acceleration of 24m s-2.what acceleration wouldit give if both the masses were tied together?
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F=ma, so
5 = 18M = 24m
M = 5/18 kg
m = 5/24 kg
For both masses,
5 = (5/18 + 5/24)a
a = 72/7 m/s^2
To determine the acceleration when both masses are tied together, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
Let's consider the two cases separately:
1. For mass M:
Given force = 5N and acceleration = 18 m/s^2.
Using Newton's second law, we can write:
5N = M * 18 m/s^2
2. For mass m:
Given force = 5N and acceleration = 24 m/s^2.
Using Newton's second law again, we have:
5N = m * 24 m/s^2
Now, we need to find the acceleration when both masses are tied together. Let's assume the total mass of the system is M + m. Since both masses are tied together, they experience the same acceleration.
Using Newton's second law for the combined system, we can write:
5N = (M + m) * a
To find the value of 'a', we need to solve the system of equations we obtained earlier by substituting one equation into the other:
M * 18 m/s^2 = m * 24 m/s^2
Simplifying the equation, we can cancel out the common factor of 6 and divide both sides by M and m:
3 * 3M = 2 * 4m
This simplifies to:
9M = 8m
Now, we substitute this relationship back into the equation:
5N = (M + m) * a
5N = (9M) * a/8
Next, we can solve for 'a':
a = (5N * 8) / (9M)
Now, we have the equation to find the acceleration when both masses are tied together. You can substitute the values of N, M, and m into this equation to calculate the final acceleration value.