A particular sprinter reaches a horizontal acceleration of 13.3 m/s2 out of the starting block. The starting block is tilted such that the vertical component of the force which the starting block exerts on the sprinter compensates for the weight of the sprinter, leading to a zero vertical acceleration. What is the magnitude of the force with which the 64 kg sprinter pushes against the starting block?
The vertical force component applied by the block is M g. The horizontal component is M a, where a = 13.3 m/s^2.
g = 9.8 m/s^2
The magnitude of the force is
F = M sqrt(a^2 + g^2)
Use the M = 64 kg and compute F
To find the magnitude of the force with which the sprinter pushes against the starting block, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a.
In this case, we are given the acceleration of the sprinter as 13.3 m/s^2 and the mass of the sprinter as 64 kg. We need to find the force (F).
Using the formula F = m * a, we can substitute the given values:
F = 64 kg * 13.3 m/s^2.
Now, we can solve this equation to find the force:
F = 851.2 N.
Therefore, the magnitude of the force with which the 64 kg sprinter pushes against the starting block is 851.2 Newtons (N).