A rock band’s tour bus, mass M, is accelerating from a stop sign at rate a when a chunk of heavy metal, mass M / 5 , falls off of the bus. The applied force acting on the bus remains unchanged.
a. Show that the bus’s acceleration is then \frac{5}{4} a .
b. If the initial acceleration of the bus is 1.2 m / s ^{2} , show that the acceleration of the bus will be 1.5 m / s ^{2} when it no longer carries the heavy metal.
2. a. Again, we’re asked to find the acceleration. From Newton’s second law we know that a=\frac{F_{\text {net }}}{m} \text {, so } F_{\text {net }}=m a \text {. }.Before the chunk of metal falls off, the mass of the bus was M, so thenet force was M a , the mass of the bus multiplied by its acceleration. We’re told that this same force acts after the metal falls off, so the final acceleration is
a =\frac{the same force}{the new mass}=\frac{M a}{M-M / 5}
=\frac{M a}{\left(\frac{5 M-M}{5}\right)}=\frac{M a}{\left(\frac{4 M}{5}\right)}=\frac{5 M a}{4 M}=\frac{5}{4} a .
It makes sense that the acceleration after the metal falls off is greater than it was initially.
b. Again, here we simply substitute the numerical
values given:
New acceleration =\frac{5}{4} a=\frac{5}{4} 1.2 m / s ^{2}=1.5 m / s ^{2},
again a reasonable answer. All the physics in both
problems occurs in part (a). The focus is on concepts
and reasoning, not on numbers. In part (b) the answer is found by substituting numerical values in the solution to part (a). Judgment about units of measurement and significant figures, and the reasonableness of an answer, can be employed in part (b).