The kinetic energy (E) of an object, in joules, is found using the formula πΈ=12ππ£2, where m is the mass in kg and v is the velocity of the object in m/s.
(a) Determine E when m = 2 kg and v = 1.2 m/s.
(b) Determine m when E = 162 joules and v = 9 m/s.
+26400 The kinetic energy (E) of an object, in joules, is found using the formula πΈ=12ππ£2, where m is the mass in kg and v is the velocity of the object in m/s.
\(E_{\text{kinetic}} = \frac{1}{2} m v^2.\)
(a) Determine E when m = 2 kg and v = 1.2 m/s.
\(\begin{array}{rcl} E &=& \frac{1}{2} \cdot m \cdot v^2 \qquad m = 2\ \mathrm{kg} \qquad v = 1.2\frac{\mathrm{m}}{\mathrm{s}}\\ E &=& \frac{1}{2} \cdot 2\ \mathrm{kg} \cdot (1.2\frac{\mathrm{m}}{\mathrm{s}})^2 \\ E &=& 1.2^2\ \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \\ E &=& 1.44 \ \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \\ \boxed{~ \begin{array}{rcl} \frac{ 1\ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} &=& 1\ J \end{array} ~}\\ \text{in joules }: \qquad E &=& 1.44 \ \ J \\ \end{array}\)
(b) Determine m when E = 162 joules and v = 9 m/s.
\(\begin{array}{rcl} E &=& \frac{1}{2} \cdot m \cdot v^2 \\ \frac{1}{2} \cdot m \cdot v^2 &=& E \\ m \cdot v^2 &=& 2 \cdot E \\ \mathbf {m} & \mathbf{=} & \mathbf{ \dfrac{ 2 \cdot E }{ v^2 }} \\ \boxed{~ \begin{array}{rcl} 1\ J &=& \frac{ 1\ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \end{array} ~}\\ m & = & \dfrac{ 2 \cdot E }{ v^2 } \qquad E=162\ \mathrm{J}=162 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \qquad v = 9\frac{\mathrm{m}}{\mathrm{s}}\\ m & = & \dfrac{ 2 \cdot 162 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} }{ (9\frac{\mathrm{m}}{\mathrm{s}})^2 } \\ m & = & \dfrac{ 324 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} }{ 81\frac{\mathrm{m^2}}{\mathrm{s^2}} } \\ m & = & 4 \dfrac{ \mathrm{\mathrm{kg}\cdot m^2\cdot s^2}}{\mathrm{s^2\cdot m^2}} \\ m & = & 4 \ \mathrm{kg} \\ \end{array}\)
+118723 Physics is SOOOO confusing!!!
(I've also been trying to learn some Physics today. )
http://web2.0calc.com/questions/heeeeeelp-got-test-tomorrow#r3
I am so confused. I thought work was measured in Joules (I sorted that out earlier today) and now you are telling me that Energy is measured in Joules. Is Work and Energy the same thing ??????
ALSO
Your formula is NOT there 
+26400 The kinetic energy (E) of an object, in joules, is found using the formula πΈ=12ππ£2, where m is the mass in kg and v is the velocity of the object in m/s.
\(E_{\text{kinetic}} = \frac{1}{2} m v^2.\)
(a) Determine E when m = 2 kg and v = 1.2 m/s.
\(\begin{array}{rcl} E &=& \frac{1}{2} \cdot m \cdot v^2 \qquad m = 2\ \mathrm{kg} \qquad v = 1.2\frac{\mathrm{m}}{\mathrm{s}}\\ E &=& \frac{1}{2} \cdot 2\ \mathrm{kg} \cdot (1.2\frac{\mathrm{m}}{\mathrm{s}})^2 \\ E &=& 1.2^2\ \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \\ E &=& 1.44 \ \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \\ \boxed{~ \begin{array}{rcl} \frac{ 1\ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} &=& 1\ J \end{array} ~}\\ \text{in joules }: \qquad E &=& 1.44 \ \ J \\ \end{array}\)
(b) Determine m when E = 162 joules and v = 9 m/s.
\(\begin{array}{rcl} E &=& \frac{1}{2} \cdot m \cdot v^2 \\ \frac{1}{2} \cdot m \cdot v^2 &=& E \\ m \cdot v^2 &=& 2 \cdot E \\ \mathbf {m} & \mathbf{=} & \mathbf{ \dfrac{ 2 \cdot E }{ v^2 }} \\ \boxed{~ \begin{array}{rcl} 1\ J &=& \frac{ 1\ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \end{array} ~}\\ m & = & \dfrac{ 2 \cdot E }{ v^2 } \qquad E=162\ \mathrm{J}=162 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} \qquad v = 9\frac{\mathrm{m}}{\mathrm{s}}\\ m & = & \dfrac{ 2 \cdot 162 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} }{ (9\frac{\mathrm{m}}{\mathrm{s}})^2 } \\ m & = & \dfrac{ 324 \frac{ \mathrm{\mathrm{kg}\cdot m^2}}{\mathrm{s^2}} }{ 81\frac{\mathrm{m^2}}{\mathrm{s^2}} } \\ m & = & 4 \dfrac{ \mathrm{\mathrm{kg}\cdot m^2\cdot s^2}}{\mathrm{s^2\cdot m^2}} \\ m & = & 4 \ \mathrm{kg} \\ \end{array}\)
+118723
Yea that 12 and 2 had me baffled. I knew no formulas had a 12 and a 2 in it like that. LOL
Thank you Heureka and thank you Alan. You are both wonderful.
It makes sense that work and energy transfer are the same thing and therefore both measured in Joules.
Thanks Alan. :))
