Determine how the force exerted on an object must be changed to reduce the object's acceleration by half.
Understand the Problem
The question is asking how to adjust the force acting on an object in order to halve the object's acceleration. It requires an understanding of Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
Answer
To halve the acceleration, reduce the force to $F_{\text{new}} = \frac{1}{2} F_{\text{original}}$.
Answer for screen readers
To reduce the object's acceleration by half, the force exerted on the object must be reduced to half, so:
$$ F_{\text{new}} = \frac{1}{2} F_{\text{original}} $$
Steps to Solve
- Identify the relationship between force, mass, and acceleration
According to Newton's second law, the relationship is given by the formula:
$$ F = ma $$
where ( F ) is force, ( m ) is mass, and ( a ) is acceleration.
- Set up the equation for the original acceleration
Assume the original acceleration of the object is ( a ), thus the original force can be expressed as:
$$ F_{\text{original}} = m \cdot a $$
- Determine the new acceleration
To halve the acceleration, the new acceleration ( a_{\text{new}} ) will be:
$$ a_{\text{new}} = \frac{a}{2} $$
- Set up the equation for the new force
Using the new acceleration, the new force can be expressed as:
$$ F_{\text{new}} = m \cdot a_{\text{new}} = m \cdot \frac{a}{2} $$
- Relate the new force to the original force
Substituting the expression for the new force gives:
$$ F_{\text{new}} = \frac{1}{2} m \cdot a = \frac{1}{2} F_{\text{original}} $$
This shows that to halve the acceleration, the force must also be halved.
To reduce the object's acceleration by half, the force exerted on the object must be reduced to half, so:
$$ F_{\text{new}} = \frac{1}{2} F_{\text{original}} $$
More Information
This demonstrates that the acceleration of an object is directly proportional to the net force acting upon it. Halving the force results in halving the acceleration, assuming mass remains constant.
Tips
- Misunderstanding that mass affects the relationship: Some may think that if they reduce force, they also need to adjust mass. In this problem, mass remains constant, so only force needs to be adjusted.
- Confusing acceleration decrease with mass decrease: It's important to note that acceleration is dependent on force and mass; halving acceleration only requires adjusting force.
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