Question

1. a boy drops his toy off the bunk bed. the distance to the floor is 2.5m. it takes 1.0s for the toy to reach the floor. gravity accelerates objects on earth at 9.8 m/s². what is the toys mass? what is the force of gravity on the toy?

Explanation:

Step1: Identify the relevant formula

The distance - time formula for free - fall motion is $d = v_0t+\frac{1}{2}gt^{2}$. Since the toy is dropped ($v_0 = 0$), the formula simplifies to $d=\frac{1}{2}gt^{2}$, and the force formula is $F = mg$. First, we need to find the time it takes for the toy to fall using $d=\frac{1}{2}gt^{2}$. Given $d = 2m$ and $g=9.8m/s^{2}$, we can solve for $t$.
$2=\frac{1}{2}\times9.8\times t^{2}$
$t^{2}=\frac{2\times2}{9.8}$
$t=\sqrt{\frac{4}{9.8}}\ s$

Step2: Find the mass using another kinematic equation (not necessary as we can directly use $F = mg$ once we know $g$ and assume we want to find the force in terms of mass). But if we assume we want to find mass from force - distance - time relations. First, from $d=\frac{1}{2}gt^{2}$, we can also use the fact that $F = mg$ and $a = g$. However, a more straightforward way is to use $F = mg$. If we assume we want to find the force on the toy, and we know $g = 9.8m/s^{2}$, and we assume the mass of the toy is $m$. But if we want to find the mass from the given distance and acceleration, we know $d=\frac{1}{2}at^{2}$ ($a = g$), and we can also use $F=ma$. In the end, the force of gravity on an object is given by $F = mg$. If we assume we want to find the force when the toy is in free - fall, and we know $g = 9.8m/s^{2}$, and we assume the mass of the toy is $m$. The force of gravity $F$ on the toy is $F = mg$. Since we are not given the mass of the toy, if we assume the mass of the toy is $m$ kg, the force of gravity on the toy is $F = 9.8m$ N. If we assume the mass of the toy is $1$ kg (for the sake of a numerical example), then $F=9.8\times1 = 9.8$ N.

Answer:

The force of gravity on the toy is $F = mg$ (where $m$ is the mass of the toy and $g = 9.8m/s^{2}$). If $m = 1$ kg, then $F = 9.8$ N.