Question

A bus travelling at constant speed of 81km/hr rounds a curve of radius 200meter. Find Centripetal Acceleration?

Answer 1

Answer:

Given:

Speed of object = 81 km/hr

Radius of curve = 200 m

To find:

Centripetal acceleration experienced by the body.

Concept:

Centripetal acceleration is a radial acceleration experienced by an object undergoing circular motion. It is directed towards the centre of the circular track.

It is the resultant of all the forces acting on the body.

Conversion :

Convert Speed from km/hr to m/s

81 km/hr = 81 × {5/18} = 22.5 m/s

Calculation:

Centripetal acc be denoted by "a".

$force = \dfrac{m {v}^{2} }{r}$

$= > acc. = \dfrac{force}{mass}$

$= > a = \dfrac{ (\dfrac{m {v}^{2} }{r} )}{m}$

$= > a = \dfrac{ {v}^{2} }{r}$

$= > a = \dfrac{ {(22.5)}^{2} }{200}$

$= > a = 2.53125 \: m {s}^{ - 2}$

So final answer :

$\boxed{ \large{ \sf{ \red{a = 2.53125 \: m {s}^{ - 2} }}}}$

Answer 2

Answer:

• The Centripetal Acceleration (a) is 2.531 m/s²

GIven:

1. Radius of Curvature (r) = 200 m.
2. Speed of bus (v) = 81 Km/h = 22.5 m/s [S.I units]

Explanation:

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From the relation we Know,

⇒ F = M v² / r

Where,

• M Denotes Mass of body
• F Denotes Centripetal Force.
• v Denotes Velocity of body.
• r Denotes radius of curvature.

Now,

⇒ F = M v² / r

Substituting the values,

⇒ F = M × (22.5)² / 200

⇒ F = M × 506.25 / 200

⇒ F = M × 2.531

⇒ F = 2.531 M

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From the relation we know,

⇒ F = M a

Where,

• F denotes Force.
• M Denotes Mass.
• a Denotes Acceleration.

Now,

⇒ F = M a

Substituting the values,

⇒ 2.531 M = M × a

⇒ a = 2.531 M / M

⇒ a = 2.531

⇒ a = 2.531 m/s²

∴ The Centripetal Acceleration (a) is 2.531 m/s².

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