What is the centripetal force acting on a bicycle/rider system with a combined mass of 90 kg and a speed of 10 m/sec turning in a circle with a radius of 20 m?

The centripetal force required to keep an object moving in a circular path is determined using the formula:

[ F_c = \frac{mv^2}{r} ]

where:

• ( F_c ) is the centripetal force,
• ( m ) is the mass of the object,
• ( v ) is the speed of the object, and
• ( r ) is the radius of the circular path.

For this bicycle/rider system:

• The mass ( m = 90 , \text{kg} ),
• The speed ( v = 10 , \text{m/s} ),
• The radius ( r = 20 , \text{m} ).

Substituting these values into the formula gives:

[ F_c = \frac{90 , \text{kg} \cdot (10 , \text{m/s})^2}{20 , \text{m}} ]

Calculating ( (10 , \text{m/s})^2 ) results in ( 100 , \text{m}^2/\text{s}^2 ). Thus, we have:

[ F_c = \frac