Question

A car is moving on a circular road of diameter 50 m with a speed 5 ms-1. It is
suddenly accelerated at a rate 1 ms-2. If mass is 500 kg, net force acting on the
car is :​

Answer 1

Answer:

Explanation:

Given :

• Diameter of a circular road (d) = 50m
• Speed of a car (v) = 5 m/s
• Interial acceleration (aₜ) = 1 m/s²
• Mass of a car (m) = 500 kg

To Find :

• Net force acting on the car, Fₙₑₜ

Solution :

★Converting unit,

$\implies \sf \: r = \dfrac{d}{2} \\ \\ \implies \sf \: r = \not \dfrac{50}{2} \\ \\ \implies \sf \green{ r = 25 \: m}$

★Radial acceleration (aᵣ),

$\implies \sf \: a_{r} = \dfrac{v {}^{2} }{r} \\ \\ \implies \sf \: a_{r} = \dfrac{5 {}^{2} }{25} \\ \\ \implies \sf \: a_{r} = \not\dfrac{25}{25} \\ \\ \implies \sf \red{ a_{r} =1 ms {}^{ - 2} }$

★Net acceleration (aₙₑₜ),

$\implies \sf \: a_{net} = \sqrt{(a_t) {}^{2} + ( \sqrt{a_r }) {}^{2} } \\ \\ \implies \sf \: a_{net} = \sqrt{1 {}^{2} + 1 {}^{2} } \\ \\ \implies \sf \: a_{net} = \sqrt{1 + 1} \\ \\ \implies \sf \purple{ a_{net} = \sqrt{2} ms^{-2} }$

★Net force (Fₙₑₜ) acting on the car,

$\implies \sf \: F_{net} = m \times a_{net} \\ \\ \implies \sf \: F_{net} = 500 \times \sqrt{2} \\ \\ \implies\sf \orange{F_{net} = 500 \sqrt{2} N}$

Answer 2

$\large\sf\underline{\color{green}{Given :}}$

• $\sf{\purple{Diameter~of~a~circular ~road~ (d) ~= ~50m}}$

• $\sf{\purple{Speed ~of ~a ~car~ (v) ~=~ 5~ m/s}}$

• $\sf{\purple{Interial ~acceleration ~(at)~ =~ 1 ~m/s²}}$

• $\sf{\purple{Mass ~of ~a ~car~ (m) ~= ~500~ kg}}$

$\large\sf\underline{\color{green}{To~Find :}}$

• $\sf{\color{royalblue}{Net~ force~ acting ~on ~the ~car~, Fnₑt}}$

$\large\sf\underline{\color{green}{Solution :}}$

Converting unit

$\begin{gathered}\implies \sf { \color{deepskyblue}\: {r = \dfrac{d}{2}}} \\ \\ \implies \sf \:{ \color{deepskyblue}{ r = \cancel \dfrac{50}{2}}} \\ \\ \boxed{\implies \sf{ \color{deepskyblue}{ r = 25 \: m}}}\end{gathered}$

Radial acceleration (aᵣ),

$\begin{gathered}\implies \sf \:{ \pink{ a_{r} = \dfrac{v {}^{2} }{r}}} \\ \\ \implies \sf \: { \pink{a_{r} = \dfrac{5 {}^{2} }{25}}} \\ \\ \implies \sf \:{ \pink{ a_{r} = \cancel\dfrac{25}{25}}} \\ \\ \: \boxed {\implies \sf \pink{ a_{r} =1 ms {}^{ - 2} }}\end{gathered}$

Net acceleration (aₙₑₜ),

$\begin{gathered}\implies \sf \:{ \color{orange}{ a_{net} = \sqrt{(a_t) {}^{2} + ( \sqrt{a_r }) {}^{2} }}} \\ \\ \implies \sf \:{ \orange{ a_{net} = \sqrt{1 {}^{2} + 1 {}^{2} } }}\\ \\ \implies \sf \:{ \orange{ a_{net} = \sqrt{1 + 1}}} \\ \\ \boxed{\implies \sf \orange{ a_{net} = \sqrt{2} ms^{-2} }}\end{gathered}$

Net force (Fₙₑₜ) acting on the car,

$\begin{gathered}\implies \sf \:{ \red{ F_{net} = m \times a_{net}}} \\ \\ \implies \sf \:{ \red{ F_{net} = 500 \times \sqrt{2}}} \\ \\ \boxed{\implies\sf \red{F_{net} = 500 \sqrt{2} N}}\end{gathered}$