Suppose that a constant force is applied to an object. Newton's Second Law of Motion states that the acceleration of the object varies inversely with its mass. A constant force acting upon an object with mass 12 kg produces an acceleration of 2m/s^2. The acceleration of another object produced by the same force is 3m/s^2. What is the mass of this object?
a = k/m^2 , where k is constant
given: when a=2 m/s^2, m = 12 kg
2 = k/12^2
k = 288
a = 288/m^2
so when a = 3
3 = 288/m^2
3m^2 = 288
m^2 = 96
m= appr 9.8
the mass is appr 9.8 Kg
or , just use a ratio
2/3 = m^2/12^2
3m^2 = 288
etc, same as above
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To find the mass of the second object, 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.
In this scenario, we know that the force acting on both objects is constant. Let's denote this force as "F" for simplicity.
According to the problem, the first object has a mass of 12 kg and an acceleration of 2 m/s^2. Using Newton's Second Law, we can write the equation as:
F = 12 kg * 2 m/s^2
Simplifying this equation, we find:
F = 24 kg·m/s^2
Now, let's find the mass of the second object. We are given that the acceleration of the second object is 3 m/s^2.
Using the same formula, we can write:
F = mass * 3 m/s^2
Since the force is the same, we can equate the two expressions for F:
24 kg·m/s^2 = mass * 3 m/s^2
Canceling out the units of m/s^2, we have:
24 kg = mass * 3
Dividing both sides by 3, we find:
mass = 24 kg / 3
Simplifying this expression, we get:
mass = 8 kg
Therefore, the mass of the second object is 8 kg.