From what maximum height can a 61 kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.65 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is 170*10^6 N/m^2, and its smallest cross-sectional area is 2.5*10^- 4 m^2
breaking force*.65=mgh
solve for h.
The equation above is correct, however, if they are asking about falling without breaking EITHER leg, you much double the breaking force, then multiply it by .65 and then solve for h
To determine the maximum height from which a person can jump without breaking a lower leg bone, we need to calculate the impact force experienced by the bone when landing.
The impact force can be calculated using the formula:
Force = mass × acceleration
In this case, acceleration can be calculated using the formula:
acceleration = (change in velocity) / (time taken)
Since we know the distance the center of mass (CM) moves during landing and the time taken to stop the motion, we can calculate the average velocity as:
average velocity = (distance moved) / (time taken)
Now, let's break down the steps:
Step 1: Calculate the average velocity
Given that the CM moves a distance of 0.65 m from the standing to seated position, we assume this distance is covered uniformly over the time taken to stop the motion. Let's assume the time taken to be 0.1 seconds.
average velocity = (0.65 m) / (0.1 s)
average velocity = 6.5 m/s
Step 2: Calculate the change in velocity
Since the person starts from rest and comes to a stop, the change in velocity is equal to the average velocity.
change in velocity = 6.5 m/s
Step 3: Calculate the acceleration
We know that acceleration is the change in velocity divided by the time taken.
acceleration = (6.5 m/s) / (0.1 s)
acceleration = 65 m/s²
Step 4: Calculate the impact force
Using the formula Force = mass × acceleration, we can calculate the force experienced by the leg bone.
mass = 61 kg (given)
Force = (61 kg) × (65 m/s²)
Force = 3965 N
Step 5: Determine the maximum height
To find the maximum height, we need to consider the work done by the force of the impact.
Work = Force × distance
The work done by the impact force is converted into gravitational potential energy when landing. So, we can set the work equal to the potential energy formula:
Work = m × g × h
Where:
m = mass of the person (61 kg)
g = acceleration due to gravity (9.8 m/s²)
h = maximum height
Setting the work equal to the potential energy:
Force × distance = m × g × h
Solving for the maximum height:
h = (Force × distance) / (m × g)
Substituting the given values:
h = (3965 N) × (0.65 m) / ((61 kg) × (9.8 m/s²))
h ≈ 4.92 meters
Therefore, a 61 kg person can jump from a maximum height of approximately 4.92 meters without breaking the lower leg bone of either leg.