Questions: Now that we have established Newton's Second Law of Motion ( ΣF=m a) what will happen to a box if I push it with 10N? Remember to switch among the tabs on your PC. a) The 5 kg box will accelerate more than the 10 kg box b) The 5 kg box will accelerate the same as the 10 kg box c) The boxes will not accelerate d) The 5 kg box will accelerate less than the 10 kg box

Solution Steps

Newton's Second Law of Motion states that the acceleration \(a\) of an object is directly proportional to the net force \(\Sigma F\) acting on it and inversely proportional to its mass \(m\). Mathematically, this is expressed as: \[ \Sigma F = m \cdot a \]

Given a force \(F = 10 \, \text{N}\), we need to determine the acceleration for two different masses: 5 kg and 10 kg.

For the 5 kg box: \[ a_1 = \frac{F}{m_1} = \frac{10 \, \text{N}}{5 \, \text{kg}} = 2 \, \text{m/s}^2 \]

For the 10 kg box: \[ a_2 = \frac{F}{m_2} = \frac{10 \, \text{N}}{10 \, \text{kg}} = 1 \, \text{m/s}^2 \]

From the calculations, the 5 kg box has an acceleration of \(2 \, \text{m/s}^2\) while the 10 kg box has an acceleration of \(1 \, \text{m/s}^2\). Therefore, the 5 kg box will accelerate more than the 10 kg box.

Final Answer