an 83.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)

Question

an 83.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)

________nm

an electron (me = 9.10939 × 10–28 g) moving at 3.90 × 106 m/s in an electron microscope

______nm

Answer 1

I don't understand what is the question? distance? in nautical meters? or nanometers? The second one makes no sense to me.

Answer 2

I'd guess N-m or work (Joules)

83kg * 9.8 * 1mi * 1609m/mi = 1,308,760 N-m

I'd have guess power, since they specified 4 minutes, but that was not part of the units, as far as I could see.

Answer 3

To convert the given measurements into nanometers (nm), we need to use the appropriate conversion factors.

For the first question, we have an athlete who is running a "4-minute mile" at a weight of 83.0 kg. We want to convert the distance from miles to nanometers.

To convert from miles to meters, we can use the conversion factor: 1 mile = 1609.344 meters.

First, let's convert the 4-minute mile into meters per second. We have 4.00 min/mile, and we want to convert this to seconds per meter by taking the inverse:

1 min = 60 seconds, so 4.00 min = 4.00 * 60 = 240 seconds.

To calculate the speed in meters per second, we divide the distance (1609.344 meters) by the time (240 seconds):

Speed = Distance / Time
Speed = 1609.344 meters / 240 seconds
Speed = 6.7056 meters per second

Now, let's convert the speed from meters per second to nanometers per second. To do this, we multiply by the conversion factor: 1 meter = 1,000,000,000 nanometers.

Speed in nanometers per second = 6.7056 meters per second * 1,000,000,000 nanometers per meter
Speed in nanometers per second = 6,705,600,000 nanometers per second

Therefore, the speed of the athlete running a 4-minute mile is approximately 6,705,600,000 nanometers per second.

For the second question, we have an electron moving at a speed of 3.90 × 10^6 m/s in an electron microscope. We want to convert this speed to nanometers per second.

To convert from meters to nanometers, we can use the conversion factor: 1 meter = 1,000,000,000 nanometers.

Speed in nanometers per second = 3.90 × 10^6 meters per second * 1,000,000,000 nanometers per meter
Speed in nanometers per second = 3.90 × 10^6 * 1,000,000,000 nanometers per second
Speed in nanometers per second = 3.9 × 10^15 nanometers per second

Therefore, the speed of the electron in the electron microscope is approximately 3.9 × 10^15 nanometers per second.

Answer 4

You just to put it into the de Broglie equation for wavelength, which is, wavelength = h/mv, where h is plank's constant 6.626x10^-34 and m is the mass in kg and v is the speed of the object in m/s. For this one obviously you will have to change the miles a minute to meters per second and then after you need to remember to change the answer from meters to nano-meters by multiplying by 1x10^9.