Question

A 250-kg motorcycle goes around an unbanked turn of radius 13.7 m at a steady 96.5 km/h. What is the magnitude of the net force on the motorcycle

Answer 1

Answer:

13,116.35N

Explanation:

Magnitude of the net force on the motorcycle is expressed as;

F = mv²/r

m is the mass of the motorcycle

v is speed = 96.5km/hr

r is the radius = 13.7m

Convert speed to m/s:

96.5km/hr = 96.5×1000/1×3600

Speed = 96500/3600

Speed = 26.81m/s

Get the magnitude of the force:

F = 250×26.81²/13.7

F = 179,694.025/13.7

F = 13,116.35N

Hence the magnitude of the net force on the motorcycle is 13,116.35N

Answer 2

The Net force on the motorcycle will be "1.31×10⁴ N".

Given:

• Mass, m = 250 kg
• Radius, r = 13.7 m
• Speed, v = 96.5 km/h

As we know, the centripetal force is given by:

→ $F = \frac{mv^2}{r}$

By substituting the values, we get

       $= \frac{(250)[96.5\times \frac{\frac{5}{18} \ m/s}{1 \ km/h} ]}{13.7}$

       $= \frac{250\times 26.8}{13.7}$

       $= 13106.57 \ N$

or,

       $= 1.31\times 10^4 \ N$

Thus the solution above is correct.

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