Question
If the force acting on a cart doubles, what happens to the cart's acce
Ask by Fuentes Gonzalez. in the United States
Jan 27,2025
Real Tutor Solution
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Answer
If the force on the cart doubles, the cart's acceleration also doubles.
Solution
According to **Newton's Second Law of Motion**, the relationship between force (\( F \)), mass (\( m \)), and acceleration (\( a \)) is given by the equation:
\[ F = m \times a \]
This equation tells us that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.
**If the force acting on the cart doubles** (assuming the mass of the cart remains constant), the equation becomes:
\[ 2F = m \times a' \]
Where \( a' \) is the new acceleration.
To find the new acceleration:
\[ a' = \frac{2F}{m} = 2 \times \left( \frac{F}{m} \right) = 2a \]
**Therefore, the cart's acceleration will double.**
**Key Point:** *Doubling the force applied to a cart (with constant mass) results in doubling its acceleration.*
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When the force acting on a cart doubles, the cart's acceleration also doubles! This is a direct consequence of Newton's second law of motion, which states that force equals mass times acceleration (F=ma). If the mass remains constant and the force is increased, the acceleration can only increase, giving that cart an extra boost to zoom along! In practical terms, think of it like pushing a shopping cart. If you give it a little shove and it rolls slowly, but then you push twice as hard, that cart will fly down the aisle! Just remember, though, if you keep increasing the force, you’ll need to consider other factors like friction and the cart’s capacity – no one wants a runaway cart!
