the velocity, v, of an object with mass, m, and kinetic energy, $e_{k}$, is given by the equation $v =…
the velocity, v, of an object with mass, m, and kinetic energy, $e_{k}$, is given by the equation $v = sqrt{\frac{2e_{k}}{m}}$. velocity is measured in m/s, mass is measured in kg, and energy is measured in j. complete the table below to show the kinetic energy and velocity of a 25 kg object.\n| $e_{k}$ | $v$ |\n| ---- | ---- |\n| | 0 |\n| | 2 |\n| 200 | |\n| | 5 |
Answer
Explanation:
Step1: Recall the kinetic - energy formula
Given $v = \sqrt{\frac{2E_k}{m}}$, we can re - arrange it to find $E_k=\frac{mv^{2}}{2}$ (by squaring both sides and cross - multiplying). Here $m = 25$ kg.
Step2: Find $E_k$ when $v = 0$
Substitute $v = 0$ and $m = 25$ into $E_k=\frac{mv^{2}}{2}$. Then $E_k=\frac{25\times0^{2}}{2}=0$.
Step3: Find $E_k$ when $v = 2$
Substitute $v = 2$ and $m = 25$ into $E_k=\frac{mv^{2}}{2}$. So $E_k=\frac{25\times2^{2}}{2}=\frac{25\times4}{2}=50$.
Step4: Find $v$ when $E_k = 200$
Given $v=\sqrt{\frac{2E_k}{m}}$, substitute $E_k = 200$ and $m = 25$. Then $v=\sqrt{\frac{2\times200}{25}}=\sqrt{16}=4$.
Step5: Find $E_k$ when $v = 5$
Substitute $v = 5$ and $m = 25$ into $E_k=\frac{mv^{2}}{2}$. So $E_k=\frac{25\times5^{2}}{2}=\frac{25\times25}{2}=312.5$.
Answer:
| $E_k$ | $v$ |
|---|---|
| $0$ | $0$ |
| $50$ | $2$ |
| $200$ | $4$ |
| $312.5$ | $5$ |