Solved Example & Practice Problems: Normal and Tangential Components (Path Variables)

Normal and Tangential Components (Path Variables) - [ Curvilinear Motion - Dynamics of Particles ]

Solved Examples for Understanding

Example 9.8.1 

An automobile is being driven along a circular track of diameter 'd'. Determine the value of 'd' if the normal component of acceleration is 2 m/s2 for a speed of 60 km/h.

Solution :

Example 9.8.2 

A car is moving with constant speed along a circular path of radius 30 m. If for safety considerations, the acceleration is not to exceed 4 g, determine the maximum speed of the car. Refer Fig. 9.8.3.

Solution : 

Given ρ = 30 m, at = 0 (constant speed)

Example 9.8.3 

A car starts from rest on a circular curve of 250 m radius and accelerates at a constant tangential acceleration 1.2 m/s2. Determine distance travelled and time taken when magnitude of total acceleration of car becomes 1.5 m/s2.

Solution: 

Given

at = 1.2 m/s2 (constant)

a = 1.5 m/s2

As tangential acceleration is constant, we can use kinematical equations in tangential direction.

u = 0, v = 15 m/s, a = 1.2 m/s2

Example 9.8.4 

A car moves on a circular path of radius 25 m, with a uniform speed of 9 m/s. Determine the total acceleration of the car. 

Solution: 

As speed is constant, at = 0

Examples for Practice

Q.1

The driver of an automobile starts from rest and increases his speed uniformly to 72 km/h in 10 seconds on a curved road of radius 500 m. Determine the magnitude of total acceleration 6 seconds after start. 

[Ans.: 2.021 m/s2]

Q.2

A speed of racing car is increasing at constant rate from 100 kmph to 120 kmph over a distance of 180 m along a curve of 240 m radius. Determine magnitude of total acceleration of car after it has travelled 120 m along the curve. 

[Ans.: 4.26 m/s2 ]

Q.3

A particle is traversing a curved path of radius of curvature 300 m with a speed 108 km/h and a tangential acceleration 4 m/s2. Determine total acceleration of the particle. 

[Ans.: a = 5 m/s2, 36.87° with êt]