What is the mass of the second object? Answer in units of kg.
A standard object defined as having a mass of exactly 8.21kg is given an acceleration of 2.47 m/s^2 when a certain force is applied to it. A second object of unknown mass acquires an acceleration of 1.0836 m/s^2 when the same force is applied to it.
This question is answered using Newton's Second Law
F = m a
where F is the applied force, m is the mass, and a is the acceleration. Using this equation, we find that the force applied to the standard mass is
F = ( 8.21 kg ) ( 2.47 m/s^2 ) = 20.28 kg m /s^2
Now we can use that force to find the mass of the second object. First we rewrite Newton's Second Law as
m = F / a
and substitute the values to find
m = ( 20.28 kg m / s^2 ) / ( 1.0836 m / s^2 )
m = 18.71 kg
Note that since the standard mass and initial acceleration are given to three significant figures, the final answer also has a precision of only three significant figures, so we should really say
m = 18.7 kg
for our final answer.
The force required to produce an accleration of 2.47 m/s^2 in a mass of 8.21 kg is given by:
F=m*a, where m is the mass of the object and a is the acceleration. m=8.21kg and a=2.47 m/s^2
Therefore, the force applied is F=8.21kg*2.47 m/s^2=20.2787 newton on the first object.
Now that we know the force we apply on the second object is the same i.e,20.2787N, and it generates an acceleration of 1.0836 m/s^2. To find the mass of the object we again use the same formula: F= mass*acceleration or F=m*a, here F=20.2787 and a =1.0836m/s^2. So,
mass = F/a=20.2787/1.0836 = 18.7142 m/s^2