Hello!
A falling piano reaches a velocity of 120 km/h. Find the kinetic energy if the mass of the piano is 357 kg.
Ek= 1/2mv^2
Ek= 1/2(357)(33m/s)^2
Ek= 194386.5 J
The problem is that my answer key has the answer 208kJ. What's my error? I have tried this problem many times. And how do I know when to use Joules or Kilojoules? Thanks!
Have you considered that the answer key is wrong?
Hello!
To calculate the kinetic energy, you have correctly used the equation Ek = 1/2mv^2, where Ek is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
However, it appears that there may be an error in the conversion of units. You mentioned that the velocity of the piano is 120 km/h, but in your calculation, you used 33 m/s as the value for v.
To convert 120 km/h to m/s, you can use the conversion factor:
1 km/h = 1000 m/3600 s
Plugging in the value, you get:
120 km/h * (1000 m/3600 s) = 33.33 m/s (rounded to two decimal places).
Using this corrected value, you can recalculate the kinetic energy:
Ek = 1/2 * (357 kg) * (33.33 m/s)^2
Ek = 1/2 * (357 kg) * (1110.94 m^2/s^2)
Ek ≈ 198,944.785 J (rounded to three decimal places).
So, the correct answer is approximately 198,944.785 J, not 194,386.5 J.
As for when to use Joules (J) or Kilojoules (kJ), it depends on the scale of the problem and the units given in the question. In scientific calculations, Joules are often used for smaller energy values, and Kilojoules are used for larger energy values. For example, if the value is given in thousands of Joules, it is more appropriate to use Kilojoules (kJ) as the unit to represent the answer. In this case, the answer 198,944.785 J can also be expressed as 198.945 kJ.
Hope this helps! Let me know if you have any further questions.