A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if The force is halved and the object's mass is doubled?

검증된 단계별 안내

Step 1: Recall Newton's Second Law of Motion, which states that the force acting on an object is equal to the product of its mass and acceleration:

F = m a

. Rearrange this equation to solve for acceleration:

a = F / m

Step 2: Identify the initial conditions. The object initially accelerates at 10 m/s² under a constant force. Using the formula for acceleration, the initial acceleration is given by

a = F / m

, where

F is the force and m is the mass.

Step 3: Analyze the new conditions. The force is halved, so the new force becomes

F /2

. The mass is doubled, so the new mass becomes

2 m

Step 4: Substitute the new force and mass into the formula for acceleration:

a = (F /2)/(2 m)

. Simplify the expression:

a = F /(4 m)

Step 5: Compare the new acceleration to the initial acceleration. Since the initial acceleration was

a = F / m

, the new acceleration is one-fourth of the initial acceleration. Therefore, the new acceleration will be

10/4

m/s².

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주요 개념

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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 force, m is the mass, and a is the acceleration. Understanding this law is crucial for analyzing how changes in force and mass affect an object's acceleration.

Force and Mass Relationship

The relationship between force, mass, and acceleration indicates that if the force applied to an object is reduced while its mass is increased, the resulting acceleration will change. Specifically, halving the force while doubling the mass leads to a new acceleration that can be calculated using the rearranged formula a = F/m. This concept is essential for predicting the object's behavior under varying conditions.

Acceleration Calculation

Acceleration is defined as the rate of change of velocity of an object over time. In this scenario, to find the new acceleration after modifying the force and mass, one can substitute the new values into the formula a = F/m. This calculation allows for a clear understanding of how the object's motion will be affected by the changes in force and mass.