Question

1. a box is pushed with a constant force of 10 n. what will happen to its acceleration?

Answer:

To determine what happens to the acceleration of the box, we use Newton's second law of motion, which is given by the formula \( F = ma \), where \( F \) is the force applied, \( m \) is the mass of the object, and \( a \) is the acceleration produced.

Step 1: Analyze the given information

We know that the force \( F \) applied to the box is constant at \( 10 \, \text{N} \). Let's assume the mass \( m \) of the box remains constant (since there's no information suggesting a change in mass).

Step 2: Rearrange the formula to solve for acceleration

From \( F = ma \), we can solve for acceleration \( a \) by dividing both sides of the equation by \( m \):
\[
a = \frac{F}{m}
\]

Step 3: Determine the effect on acceleration

Since the force \( F \) is constant and the mass \( m \) is also constant (assuming no change in the box's mass), the acceleration \( a \) will remain constant as well. This is because acceleration is directly proportional to the force applied (\( a \propto F \)) and inversely proportional to the mass (\( a \propto \frac{1}{m} \)). If both \( F \) and \( m \) are constant, the ratio \( \frac{F}{m} \) (which is the acceleration) will not change.

However, if the mass were to change (for example, if we add or remove something from the box), the acceleration would change. But with the given information (constant force and no mention of mass change), the acceleration remains constant as long as the mass of the box does not change.

If we consider a scenario where the mass might change (though not indicated here), for example, if the box is being filled or emptied while the force remains \( 10 \, \text{N} \):

• If the mass \( m \) increases, then from \( a = \frac{F}{m} \), the acceleration \( a \) would decrease (since \( F \) is constant and \( m \) is in the denominator).
• If the mass \( m \) decreases, the acceleration \( a \) would increase.

But based on the problem statement (only a constant force of \( 10 \, \text{N} \) is mentioned, with no change in mass), the acceleration of the box will remain constant (assuming the mass of the box does not change). If we assume the mass is constant, the acceleration is \( a=\frac{10}{m} \) (in \( \text{m/s}^2 \)) and will not change as long as \( F \) and \( m \) are constant.

If we consider the general case without assuming mass is constant:
The acceleration of the box is directly proportional to the net force acting on it and inversely proportional to its mass (\( a=\frac{F_{\text{net}}}{m} \)). Since the applied force is constant at \( 10 \, \text{N} \), if the mass of the box remains constant, the acceleration will remain constant. If the mass changes, the acceleration will change inversely with the mass (increase if mass decreases, decrease if mass increases). But with the given information (only constant force, no mass change), we can say that if the mass of the box does not change, the acceleration will remain constant. If we consider the initial situation (before any mass change), the acceleration is determined by \( a = \frac{10}{m} \) and will stay the same as long as \( F \) and \( m \) are constant.

In most basic physics problems like this, when only a constant force is mentioned and no mass change is indicated, we assume the mass is constant, so the acceleration will remain constant (or more precisely, it will have a constant value determined by the force and the mass of the box).

If we want to express the acceleration in terms of mass, it is \( a=\frac{10}{m} \) (in SI units, where \( F \) is in Newtons, \( m \) in kilograms, and \( a \) in \( \text{m/s}^2 \)). So, as long as \( F = 10 \, \text{N} \) (constant) and \( m \) (mass) is constant, the acceleration \( a \) will be constant. If the mass were to change, the acceleration would change accordingly (inversely proportional to the mass).

Final Answer

If the mass of the box remains constant, the acceleration of the box will remain constant (with a value of \( \boldsymbol{\frac{10}{m} \, \text{m/s}^2} \), where \( m \) is the mass of the box in kilograms). If the mass changes, the acceleration will change inversely with the mass (increase if mass decreases, decrease if mass increases). For the given problem (with a constant force of \( 10 \, \text{N} \) and assuming no change in mass), the acceleration will remain constant.