A sprinter of mass 63.7 kg runs at a constant speed of 10.2 m/s in a straight line. Find the extra force the sprinter must exert on the ground to round a curve of radius 10.8 m.
To find the extra force the sprinter must exert on the ground to round a curve of radius 10.8 m, we need to consider the centripetal force acting on the sprinter.
Centripetal force is the force that keeps an object moving in a curved path and is directed towards the center of the circle. In this case, the centripetal force is provided by the friction between the sprinter's foot and the ground.
The formula for centripetal force is given by:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the sprinter, v is the speed of the sprinter, and r is the radius of the curvature.
Plugging in the given values:
m = 63.7 kg (mass of the sprinter)
v = 10.2 m/s (speed of the sprinter)
r = 10.8 m (radius of the curvature)
F = (63.7 kg * (10.2 m/s)^2) / 10.8 m
Now, we can calculate the value of F:
F = (63.7 kg * 104.04 m^2/s^2) / 10.8 m
F = 6165.708 kg⋅m/s^2
Hence, the extra force the sprinter must exert on the ground to round the curve is approximately 6165.708 N.