A sprinter of mass 70.7 kg runs at a constant speed of 10.5 m/s in a straight line. Find the extra force the sprinter must exert on the ground to round a curve of radius 10.6 m.
what is mass*velocity^2/radius ?
To find the extra force the sprinter must exert on the ground to round a curve, we need to understand the physics concept of centripetal force.
Centripetal force is the force that keeps an object moving in a curved path and is directed towards the center of the curve. In this case, the centripetal force is provided by the friction between the sprinter's feet and the ground.
The centripetal force required to keep an object moving in a circle can be calculated using the formula:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius of the curve
In this case, the mass of the sprinter is 70.7 kg, the velocity is 10.5 m/s, and the radius of the curve is 10.6 m.
Plugging in these values into the formula, we get:
F = (70.7 kg * (10.5 m/s)^2) / 10.6 m
F = (70.7 kg * 110.25 m^2/s^2) / 10.6 m
F = 7386.675 kg * m/s^2 / m
F = 696.3 N
Therefore, the extra force the sprinter must exert on the ground to round the curve of radius 10.6 m is approximately 696.3 N.