A tractor pulls a harrow (a ploughing tool) of mass m1 with a net force F. Class 9

A tractor pulls a harrow (a ploughing tool) of mass m₁ with a net force F. Class 9

Question 1.

A tractor pulls a harrow (a ploughing tool) of mass m₁ with a net force F resulting in an acceleration of a₁. The same tractor pulls a trolley of mass m₂ with a force F producing an acceleration of a₂. If the tractor now pulls the trolley with the harrow placed on it (with the same force F), then obtain an expression for the resulting acceleration in terms of a₁ and a₂. Ignore friction. Class 9

Answer:

For harrow alone: F = m₁a₁ → m₁ = [latex]\frac{\mathrm{F}}{a_1}[/latex]

For trolley alone: F = m₂a₂ → m₂ = [latex]\frac{\mathrm{F}}{a_2}[/latex]

Combined mass = m₁ + m₂

= [latex]\frac{\mathrm{F}}{a_1}[/latex] + [latex]\frac{\mathrm{F}}{a_2}[/latex]

= [latex]\frac{\mathrm{F}\left(a_1+a_2\right)}{\left(a_1 a_2\right)}[/latex]

Acceleration when combined:

a = [latex]\frac{\mathrm{F}}{\left(m_1+m_2\right)}[/latex]

= [latex]\frac{\mathrm{F}}{\left[\frac{\mathrm{~F}\left(a_1+a_2\right)}{\left(a_1 a_2\right)}\right]}[/latex]

a = [latex]\frac{\left(a_1 a_2\right)}{\left(a_1+a_2\right)}[/latex]