A Princeton prof. (mass = 67.0 kg), surprised by the large stopping force he calculates for jumping flat footed from a height of 0.11 m, decides to try the experiment. Calculate he deceleration (in g's) if he stops in a distance of 0.30 cm. (Do not try this. You could easily break an ankle!)

Question

A Princeton prof. (mass = 67.0 kg), surprised by the large stopping force he calculates for jumping flat footed from a height of 0.11 m, decides to try the experiment. Calculate he deceleration (in g's) if he stops in a distance of 0.30 cm. (Do not try this. You could easily break an ankle!)

Answer 1

Potential energy mgh

work stopping: force*distance

set them equal.

Answer 2

yeah you wanna do that and tell me what you get or just tell me what you used for the masses because i keep getting wrong.

Answer 3

i've gotten 41.57 41.92 and 5.68 when i only used the mass of the bullet

Answer 4

mass of the bullet? come back to planet Earth.

Force=massman*g*height/distance

put height and distance in meters.

Answer 5

ha wrong question sorry.

Answer 6

To calculate the deceleration experienced by the Princeton professor, we can use the equations of motion.

First, we need to convert the distance of 0.30 cm to meters by dividing it by 100:

Distance = 0.30 cm / 100 = 0.003 m

Next, we need to determine the initial velocity (v0) before the professor began to decelerate. Since the professor jumped flat-footed from a height of 0.11 m, we can use the equation for gravitational potential energy to find the initial velocity:

Potential Energy (PE) = Mass (m) * Gravity (g) * Height (h)

PE = m * g * h

Here, m = 67.0 kg, g = 9.8 m/s^2, and h = 0.11 m.

PE = 67.0 kg * 9.8 m/s^2 * 0.11 m

Next, we can equate the potential energy to the kinetic energy at the moment just before the professor starts decelerating:

PE = KE

m * g * h = (1/2) * m * v0^2

Simplifying, we find:

v0 = sqrt(2 * g * h)

Plugging in the values, we get:

v0 = sqrt(2 * 9.8 m/s^2 * 0.11 m)

Now that we have the initial velocity, we can calculate the deceleration using the equation:

v^2 = v0^2 + 2 * a * d

Here, v = 0 (the professor stops), v0 is the initial velocity, a is the deceleration, and d is the distance over which the deceleration occurs.

Rearranging the equation to solve for a, we get:

a = (v^2 - v0^2) / (2 * d)

Plugging in the values, we get:

a = (0 - v0^2) / (2 * 0.003 m)

Finally, solve for a:

a = - v0^2 / (2 * 0.003 m)

Now, we can calculate the deceleration (a) in terms of g (acceleration due to gravity). Since g = 9.8 m/s^2, we can convert the deceleration to g's by dividing the value of a by 9.8 m/s^2.

a (in g's) = a / 9.8 m/s^2

Now, you can substitute the value of a into the equation above and calculate the deceleration in g's.