Question

A1500kg automobile travels eastward at speed of 8m/s it makes a 90°turn to the north in a time of 3 s and continues with the same speed find
a) impulse delivered to the car as a result of the turn
b) average force exerted in the car during the turn
c) average force of the car in the road during the turn

Answer 1

Given:-

The mass of Automobile = 1500 Kg

Angle $(\theta) = 90^{\circ}$

Initial velocity $(\mathsf{U}) = 8\mathsf{m / s}$

Time taken (t) = 3 sec.

Now,

Consider the east direction as $x$-axis then

Initial velocity $(\underline{\mathsf{U}}) = 8\mathsf{m / s}$ (i) in east-direction

Final velocity $(\mathsf{v}) = 8\mathsf{m / s}$ (j) in north-direction

A) Find the impulse delivered to the car as a result of the turn

Impulse (I) = Change in momentum

$$\mathrm{Impulse(i)} = m \left(8 \frac{m}{s} i - \frac{8m}{s} j\right)$$

The magnitude of the in impulse is (I) = $m \times \sqrt{8^2 + 8^2}$

$$\begin{array}{l} = 1500 \times 11.313 \\ = 16970.56 \text{ Kg. m/s (North - south direction)} \end{array}$$

B) Find the average force exerted on the car during the turn.

The average force (F) = $\frac{l}{t}$

$$\begin{array}{l} = \frac{16970.56}{3} \\ = 5656.85 \text{ N} \end{array}$$

C) Find the average force exerted on the car on the road during the turn.

The average force applied by the car on the road = Force applied by the road on the car

So, Average force = 5656.85 N.

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