Question

1. a 10 - n block and a 1 - n block lie on a horizontal frictionless table. to push them with equal acceleration, we would have to push with a) equal forces on each block. b) 10 times as much force on the heavier block. c) 10 squared or 100 times as much force on the heavier block. d) one - tenth as much force on the heavier block. e) none of the above

Explanation:

Step1: Recall Newton's second - law

Newton's second - law is $F = ma$, where $F$ is the force, $m$ is the mass, and $a$ is the acceleration.

Step2: Express mass in terms of weight

Weight $W=mg$, so $m=\frac{W}{g}$. Let $W_1 = 10N$ and $W_2 = 1N$. Then $m_1=\frac{W_1}{g}$ and $m_2=\frac{W_2}{g}$.

Step3: Calculate forces for equal acceleration

If $a_1=a_2 = a$, from $F = ma$, we have $F_1=m_1a=\frac{W_1}{g}a$ and $F_2=m_2a=\frac{W_2}{g}a$. Then $\frac{F_1}{F_2}=\frac{\frac{W_1}{g}a}{\frac{W_2}{g}a}=\frac{W_1}{W_2}$. Since $\frac{W_1}{W_2}=\frac{10N}{1N}=10$, $F_1 = 10F_2$. That is, we need 10 times as much force on the heavier block.

Answer:

B. 10 times as much force on the heavier block