When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain force acts upon an object with mass 3kg, the acceleration of the object is 22m per second squared. When the same force acts upon another object, its acceleration is 33mper second squared. What is the mass of this object
We can use the formula for inverse variation, which states that if two variables, acceleration (a) and mass (m), are inversely proportional, then their product is a constant:
a * m = k
where k is the constant of variation.
We can use the given information to set up two equations using this formula:
22 * 3 = k
33 * m = k
Solving the first equation for k:
k = 22 * 3
k = 66
Substituting this value of k into the second equation:
33 * m = 66
Solving for m:
m = 66 / 33
m = 2
The mass of the object is 2 kg.
To find the mass of the second object, we can use the relationship between force, mass, and acceleration which states that acceleration is inversely proportional to mass.
Let's denote the mass of the second object as m2.
From the given information, we have:
Force = Constant (k)
For the first object:
Mass (m1) = 3 kg
Acceleration (a1) = 22 m/s^2
For the second object:
Mass (m2) = ?
Acceleration (a2) = 33 m/s^2
Using the formula for the relationship between force, mass, and acceleration:
Force = mass × acceleration
For the first object:
k = m1 × a1
For the second object:
k = m2 × a2
Since the constant force acting on the objects is the same, we can equate the expressions for k:
m1 × a1 = m2 × a2
Substituting the given values:
3 kg × 22 m/s^2 = m2 × 33 m/s^2
Simplifying the equation:
66 kg·m/s^2 = 33 m2·m/s^2
Cancelling out the units:
66 kg = 33 m2
Dividing both sides by 33:
m2 = 66 kg / 33
m2 = 2 kg
Therefore, the mass of the second object is 2 kg.