When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass
22 kg
, the acceleration of the object is
2 /ms2
. When the same force acts upon another object, its acceleration is
11 /ms2
. What is the mass of this object?
Using the formula for acceleration with a constant force:
a = F/m
We can set up a proportion between the accelerations and masses of the two objects:
2/22 = 11/m
Simplifying, we can cross-multiply to get:
2m = 242
Dividing by 2 on both sides:
m = 121
Therefore, the mass of the second object is 121 kg.
To solve this problem, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) times the acceleration (a):
F = m * a
We are given that a certain force is applied to an object with a mass of 22 kg and accelerates at 2 m/s^2. We can use this information to find the force (F) acting on the object.
F = m * a
F = 22 kg * 2 m/s^2
F = 44 N
Now we know the force acting on the first object is 44 N.
We are also given that the same force is applied to another object with an unknown mass (m) and it accelerates at 11 m/s^2. We can use this information to find the mass of the second object.
F = m * a
44 N = m * 11 m/s^2
To solve for mass (m), we rearrange the equation:
m = F / a
m = 44 N / 11 m/s^2
m = 4 kg
Therefore, the mass of the second object is 4 kg.