Question

Q-4 A force of 5 N applied on m1 produces an acceleration of 8 m/s2 and when applied on m2 produces an acceleration of 24 m/s2. When they are tied together, what will be the acceleration? please do it​

Answer 1

Provided that:

★ According to case first!

• Force = 5 Newton
• Acceleration = 8 m/s sq.

★ According to case second!

• Force = 5 Newton
• Acceleration = 24 m/s sq.

To determine:

• The acceleration when the both masses are tied together!?

Solution:

• The acceleration when the both masses are tied together = 6.09 metre per second sq.

Using concepts:

• Second law of motion that tell us about the formula to calculate the force.

• Total mass formula.

Using formulas:

• Second law of motion that tell us about the formula to calculate the force:

• ${\small{\underline{\boxed{\pmb{\sf{F \: = ma}}}}}}$

Where, a denotes acceleration, F denotes force and m denotes mass.

• Total mass is given by the mentioned formula:

• ${\small{\underline{\boxed{\pmb{\sf{M'' \: = m + m'}}}}}}$

Where, M′′ denotes total mass, m denotes mass first and m′ denotes mass second.

Required solution:

† Case number first!

~ Firstly let us find out the mass of the body in condition first by using suitable force formula!

$:\dashrightarrow \sf Force \: = Mass \times Acceleration \\ \\ :\dashrightarrow \sf F \: = ma \\ \\ :\dashrightarrow \sf 5 = m(8) \\ \\ :\dashrightarrow \sf 5 = m \times 8 \\ \\ :\dashrightarrow \sf \dfrac{5}{8} \: = m \\ \\ :\dashrightarrow \sf 0.62 \: = m \\ \\ :\dashrightarrow \sf m \: = 0.62 \: kg \\ \\ :\dashrightarrow \sf Mass \: = 0.62 \: kg$

† Case number second!

~ Now let us find out the mass of the body in condition second by using suitable force formula!

$:\dashrightarrow \sf Force \: = Mass' \times Acceleration \\ \\ :\dashrightarrow \sf F \: = m'a \\ \\ :\dashrightarrow \sf 5 = m(24) \\ \\ :\dashrightarrow \sf 5 = m' \times 24 \\ \\ :\dashrightarrow \sf \dfrac{5}{24} \: = m' \\ \\ :\dashrightarrow \sf 0.20 \: = m' \\ \\ :\dashrightarrow \sf m' \: = 0.20 \: kg \\ \\ :\dashrightarrow \sf Mass' \: = 0.20 \: kg$

___________________________

~ Now let us find out the total mass as they tied together!

$:\dashrightarrow \sf M'' \: = m + m' \\ \\ :\dashrightarrow \sf M'' = 0.62 + 0.20 \\ \\ :\dashrightarrow \sf M'' = 0.82 \: kg \\ \\ :\dashrightarrow \sf Total \: mass = 0.82 \: kg$

~ Now let us find out the acceleration when they tied together by again using force suitable formula!

$:\dashrightarrow \sf Force \: = Mass'' \times Acceleration \\ \\ :\dashrightarrow \sf F \: = m''a \\ \\ :\dashrightarrow \sf 5 = 0.82(a) \\ \\ :\dashrightarrow \sf 5 = 0.82 \times a \\ \\ :\dashrightarrow \sf \dfrac{5}{0.82} \: = a \\ \\ :\dashrightarrow \sf 6.09 \: = a \\ \\ :\dashrightarrow \sf a \: = 6.09 \: ms^{-2} \\ \\ :\dashrightarrow \sf Acceleration \: = 6.09 \: ms^{-2}$