Final answer:
The quadriceps femoris are the muscles used by a soccer player to straighten the right leg to kick the ball. They produce the force to achieve the necessary angular acceleration during kicking, given the moment of inertia and lever arm distance involved.
Step-by-step explanation:
The muscles that a soccer player uses to straighten the right leg to kick the ball are the quadriceps femoris. This group of muscles is located in the anterior compartment of the thigh and consists of four muscles which are the main extensors of the knee joint. They exert the force necessary to produce the angular acceleration required for the kicking motion.
According to the given problem, the soccer player achieves an angular acceleration of 30.00 rad/s² for her lower leg, which has a moment of inertia of 0.750 kg. m². To find the force exerted by the muscle during the kick, we can use the equation τ = I×α, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. The force can then be calculated from the torque using the lever arm distance from the point of rotation to the point of force application, which is given as 1.90 cm. Therefore, the force (F) is calculated by rearranging the formula to F = τ/r, where τ is the torque obtained from I×α and r is the lever arm distance in meters.
It's important to note that the weight of the leg can be neglected when calculating the torque because it exerts no torque when the center of gravity of the lower leg is directly beneath the pivot in the knee. Also, the exerted force by the quadriceps is significantly greater than the torque created by the weight of the lower leg during rotation.