Question

a boy drops his toy off the bunk bed. the distance to the floor is 2.5m. it takes 0.71 seconds to reach the floor. gravity acceleration objects on earth at 9.8 m/s². the earths gravity applies 5.0 newtons of force to the toy. what is the toys mass?

Explanation:

Step1: Identify the relevant kinematic - equation

The vertical - motion of the toy is a free - fall motion. The kinematic equation for vertical displacement $h = v_0t+\frac{1}{2}gt^2$. Since the toy is dropped ($v_0 = 0$), the equation simplifies to $h=\frac{1}{2}gt^2$. We can first find the time $t$ it takes for the toy to fall.
$h = 2.8m$ and $g = 9.8m/s^2$. From $h=\frac{1}{2}gt^2$, we can solve for $t$:
$t=\sqrt{\frac{2h}{g}}$.

Step2: Calculate the time

Substitute $h = 2.8m$ and $g = 9.8m/s^2$ into the formula for $t$:
$t=\sqrt{\frac{2\times2.8}{9.8}}=\sqrt{\frac{5.6}{9.8}}\approx\sqrt{0.5714}\approx0.756s$.

Step3: Use Newton's second - law

Newton's second - law is $F = ma$, where in the case of free - fall near the Earth's surface, $a = g$ and $F$ is the force of gravity. We know $F = 5.0N$ and $g = 9.8m/s^2$. From $F=mg$, we can solve for the mass $m$.
$m=\frac{F}{g}$.

Step4: Calculate the mass

Substitute $F = 5.0N$ and $g = 9.8m/s^2$ into the formula for $m$:
$m=\frac{5.0}{9.8}\approx0.51kg$.

Answer:

$0.51kg$