The foot of a 55 kg sprinter is on the ground for 0.25 s while her body accelerates from rest to 2.0 m/s. What is the magnitude of the friction force?

검증된 단계별 안내

Identify the known quantities: The mass of the sprinter is \( m = 55 \; \text{kg} \), the time during which the foot is on the ground is \( t = 0.25 \; \text{s} \), and the final velocity is \( v_f = 2.0 \; \text{m/s} \). The initial velocity is \( v_i = 0 \; \text{m/s} \).

Calculate the acceleration of the sprinter using the kinematic equation \( a = \frac{v_f - v_i}{t} \). Substituting the known values, \( a = \frac{2.0 - 0}{0.25} \).

Determine the net force acting on the sprinter using Newton's second law, \( F = m \cdot a \). Substituting the values for \( m \) and \( a \), \( F = 55 \cdot a \).

Recognize that the net force in this case is provided by the friction force between the sprinter's foot and the ground. Therefore, the magnitude of the friction force is equal to the net force calculated in the previous step.

Substitute the value of \( a \) from step 2 into the equation for \( F \) to find the magnitude of the friction force. Ensure the units are consistent and the result is expressed in newtons (N).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. In this scenario, understanding this law is crucial to calculate the net force acting on the sprinter as she accelerates.

Friction Force

Friction force is the resistance that one surface or object encounters when moving over another. It is influenced by the nature of the surfaces in contact and the normal force acting between them. In this problem, the friction force is essential for providing the necessary acceleration to the sprinter, allowing her to reach a speed of 2.0 m/s.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In this case, the kinematic equation can be used to determine the acceleration of the sprinter, which is necessary to find the net force and subsequently the friction force acting on her.