Question

1. the cart plus the metal cylinder in the cart will have a combined mass of 0.600 kg. time how long it takes the cart to travel from the time the counterweight is released to the time the counterweight hits the ground. use this information to fill out the table below.

counterweight used	net force (σf) applied to the cart (n)	combined mass of the cart and metal cylinder (kg)	calculated acceleration (a) of the cart (m/s²)	time from release of counterweight to it hitting the ground (s)
100 g

page # 1 of 2

$vec{a}=\frac{sigmavec{f}}{m}$

Explanation:

Step1: Convert counter - weight mass to kg

For 50 g, $m_1 = 50\times10^{- 3}\text{ kg}=0.05\text{ kg}$; for 100 g, $m_2 = 100\times10^{-3}\text{ kg}=0.1\text{ kg}$.

Step2: Calculate net force

The net force applied to the cart is equal to the weight of the counter - weight. Using $F = mg$ (where $g = 9.8\text{ m/s}^2$). For 50 g counter - weight, $F_1=m_1g=0.05\times9.8 = 0.49\text{ N}$; for 100 g counter - weight, $F_2=m_2g=0.1\times9.8 = 0.98\text{ N}$.

Step3: Calculate acceleration

Using $\vec{a}=\frac{\sum F}{m}$, with combined mass $m = 0.600\text{ kg}$. For 50 g counter - weight, $a_1=\frac{F_1}{m}=\frac{0.49}{0.600}\approx0.817\text{ m/s}^2$; for 100 g counter - weight, $a_2=\frac{F_2}{m}=\frac{0.98}{0.600}\approx1.633\text{ m/s}^2$.

Step4: Assume the height $h$ from which counter - weight falls is known (not given in problem, assume $h$). Using $h = v_0t+\frac{1}{2}at^{2}$, since $v_0 = 0$, we have $t=\sqrt{\frac{2h}{a}}$. If we assume $h = 1\text{ m}$ for example. For 50 g counter - weight, $t_1=\sqrt{\frac{2\times1}{0.817}}\approx1.57\text{ s}$; for 100 g counter - weight, $t_2=\sqrt{\frac{2\times1}{1.633}}\approx1.11\text{ s}$.

Counter - weight used	Net Force ($\sum F$) applied to the cart (N)	Combined mass of the cart and metal cylinder (kg)	Calculated acceleration ($a$) of the cart ($\text{m/s}^2$)	Time from release of counter - weight to it hitting the ground (s) (assuming $h = 1\text{ m}$)
100 g	0.98	0.600	1.633	1.11

Answer:

Counter - weight used	Net Force ($\sum F$) applied to the cart (N)	Combined mass of the cart and metal cylinder (kg)	Calculated acceleration ($a$) of the cart ($\text{m/s}^2$)	Time from release of counter - weight to it hitting the ground (s) (assuming $h = 1\text{ m}$)
100 g	0.98	0.600	1.633	1.11