a forceof 10 n
acts on a masses on
& m2 to acceleration them 2m/s2 and
4 m/s2. if they are tied together
find the acceleration.
Answers
Answer:
A force of 10 N is applied on 2 bodies of masses m1 and m2 in order to accelerate them at 2 m/s² and 4 m/s² .
Required to find :-
Acceleration of the bodies when they are tied to together ?
Formula used :-
\boxed{\tt{mass = \frac{force}{acceleration} }}
mass=
acceleration
force
Solution :-
Given information :-
A force of 10 N is applied on 2 bodies of masses m1 and m2 in order to accelerate them at 2 m/s² and 4 m/s² .
From the given information we can conclude that ;
Case - 1
Force ( F1 ) = 10 N
Acceleration ( a1 ) = 2 m/s²
Case - 2
Force ( F2 ) = 10 N
Acceleration ( a2 ) = 4 m/s²
We need to find the masses of the respective bodies in 2 cases
So,
In case - 1
Force ( F1 ) = 10 N
Acceleration ( a1 ) = 2 m/s²
Using the formula,
\boxed{\tt{Mass = \dfrac{Force}{Acceleration} }}
Mass=
Acceleration
Force
arrow{\tt{ Mass = \dfrac{ 10 }{ 2 } }}arrowMass=
2
10
arrow{\tt{ {M}_{1} = 5 \ kg }}arrowM
1
=5 kg
Similarly,
In case - 2
Force ( F2 ) = 10 N
Acceleration ( a2 ) = 4 m/s²
Using the same formula,
arrow{\tt{ Mass = \dfrac{ 10}{ 4 } }}arrowMass=
4
10
arrow{\tt{ {M}_{2} = 2.5 }}arrowM
2
=2.5
Now,
we need to find the acceleration when the two bodies are tied together ;
This means that we need to divide the Force by sum of the masses of two bodies ( Total Mass ) .
Hence,
Total mass = m1 + m2
=> 5 + 2.5
=> 7.5 kg
However,
\tt{ Acceleration = \dfrac{ 10 }{ 7.5 } }Acceleration=
7.5
10
Multiply the numerator and denominator with 10
So,
\tt{ Acceleration = \dfrac{ 10 \times 10 }{ 7.5 \times 10 } }Acceleration=
7.5×10
10×10
\tt{ Acceleration = \dfrac{ 100 }{ 75 }}Acceleration=
75
100
\tt{ Acceleration = 1.333 \dots }Acceleration=1.333…
\implies{\underline{\rm{ Acceleration = 1.33 \ m/s^2 \; ( approximately ) }}}⟹
Acceleration=1.33 m/s
2
(approximately)
Therefore,
Acceleration caused when two bodies are tied together = 1.33 m/s² ( approximately )
Explanation:
MARK ME AS BRAINLIST