How much force does the astronaut exert on his chair while accelerating straight up at 10 m/s²?

검증된 단계별 안내

Step 1: Identify the forces acting on the astronaut. The two forces involved are the gravitational force (weight) and the force due to the upward acceleration. The net force exerted by the astronaut on the chair will be the sum of these forces.

Step 2: Write the formula for gravitational force: \( F_{gravity} = m \cdot g \), where \( m \) is the mass of the astronaut and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

Step 3: Write the formula for the force due to upward acceleration: \( F_{acceleration} = m \cdot a \), where \( a \) is the upward acceleration (given as \( 10 \, \text{m/s}^2 \)).

Step 4: Add the two forces together to find the total force exerted by the astronaut on the chair: \( F_{total} = F_{gravity} + F_{acceleration} \). Substitute the expressions for \( F_{gravity} \) and \( F_{acceleration} \) into this equation: \( F_{total} = m \cdot g + m \cdot a \).

Step 5: Factor out \( m \) from the equation: \( F_{total} = m \cdot (g + a) \). To find the force, you need the astronaut's mass \( m \), which should be provided or assumed in the problem.

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주요 개념

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Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is fundamental in understanding how forces affect the motion of objects, including the astronaut in the question, as it allows us to calculate the force exerted based on the mass and the acceleration experienced.

Weight and Normal Force

Weight is the force exerted by gravity on an object, calculated as the product of mass and gravitational acceleration (W = mg). When an astronaut accelerates upwards, the normal force exerted by the chair must counteract both the weight of the astronaut and provide the additional force needed for upward acceleration, which is crucial for determining the total force exerted on the chair.

Acceleration due to Gravity

Acceleration due to gravity is the rate at which an object accelerates towards the Earth, approximately 9.81 m/s². In the context of the astronaut's upward acceleration, this gravitational force must be considered alongside the upward acceleration to find the total force exerted on the chair, as it influences the net force acting on the astronaut.