Question

1. critical thinking you have a job loading inventory onto trucks at a meat warehouse. each truck has a weight limit of 10,000 n of cargo. you push each crate of meat along a low - resistance roller belt to a scale and weigh it before moving it onto the truck. one night, right after you weigh a 1000 - n crate, the scale breaks. describe a way in which you could apply newtons laws to approximate the masses of the remaining crates.

Explanation:

Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration) can be used. Since weight \(W=mg\) (where \(g = 9.8\space m/s^{2}\) is the acceleration due to gravity), for the known - weight crate (\(W_1=1000\space N\)), its mass \(m_1=\frac{W_1}{g}\).

Push the known - mass crate (\(m_1\)) and an unknown - mass crate (\(m_2\)) with the same force \(F\) (by applying the same push, assuming constant force over a short distance on the low - resistance roller belt). Measure the accelerations \(a_1\) and \(a_2\) of the two crates (for example, by timing how long it takes them to move a certain distance on the roller belt, \(x = v_0t+\frac{1}{2}at^{2}\), assuming \(v_0 = 0\), \(x=\frac{1}{2}at^{2}\), so \(a=\frac{2x}{t^{2}}\)).

From \(F = m_1a_1\) and \(F = m_2a_2\) (since the force \(F\) is the same for both pushes), we have \(m_1a_1=m_2a_2\), and \(m_2=\frac{a_1}{a_2}m_1\). Then, the weight of the unknown crate \(W_2 = m_2g=\frac{a_1}{a_2}m_1g=\frac{a_1}{a_2}W_1\)

Answer:

Push the \(1000 - N\) crate and an unknown - weight crate with the same force. Measure their accelerations. Use \(m_2=\frac{a_1}{a_2}m_1\) (from \(F = m_1a_1=m_2a_2\)) and \(W_2=\frac{a_1}{a_2}W_1\) (since \(W = mg\)) to find the weight (and thus mass) of the unknown crate.