Question

A 900 kg car moving at 20 m/s takes a turn around a circle with a radius of 40 m.Find its acceleration and the net force acting upon the car.
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Answer 1

Given :-

• Mass of the car = 900 kg
• Speed of the car = 20 m/s
• Radius of the circular track = 40 m

To find :-

• Acceleration
• Net force acting on the car

Solution :-

The car will continue to move in a straight line until and unless a external force is acting on it

In this case the force acting on the car is called as centripetal force

When the car moves in circular motion an acceleration is acting on the car towards the center of the circle

The centripetal acceleration is given by the formula ,

$\bigstar\boxed{\mathtt{ a_c = \dfrac{v^{2}}{r} }}$

Now let's substitute the given values in the above equation ,

$\implies\mathtt{ a_c = \dfrac{400}{40} }$

$\implies\mathtt{ a_c =10 \dfrac{ m }{ {s}^{2} } }$

The acceleration of the car is 10 m /s²

______________

Net force acting on the car

$\implies \mathtt{ ma_c}$

$\implies \mathtt{ 900 \times 10}$

$\implies \mathtt{ 9000 \: N}$

The net force acting on the car = 9000 N