Calculate: 5656

Janko is skating at a speed of 18 km/h. Its kinetic energy is 0.5 kJ. Janko weighs 40 kg.
Calculate:
1. what work will the braking forces do before Janko stops?
2. How big is the braking force when Janko stops after crossing a track of 14 m.?

Correct answer:

W =  0.5 kJ
F =  128.5714 N

Step-by-step explanation:

$$\begin{gathered} v=18\text{km/h} \\ {v}_1=18/3.6=5\text{m/s} \\ m=40\text{kg} \\ E=0.5\cdot m\cdot v_1^2=0.5\cdot 40\cdot 5^2=500\text{J} \\ W=E/1000=500/1000=0.5\text{kJ} \end{gathered}$$

$$\begin{gathered} s=14\text{m} \\ s=vt/2 \\ t=2\cdot s/v_1=2\cdot 14/5=\frac{28}{5}=5.6\text{s} \\ a=v/t=18/5.6=\frac{45}{14}\doteq 3.2143{\text{m/s}}^2 \\ F=m\cdot a=40\cdot 3.2143=128.5714\text{N} \end{gathered}$$

Try another example