Severe stresses can be produced in the joints by jogging on hard surfaces or with insufficiently padded shoes.If the downward velocity of the leg is 7.3m/s when the joggers foot hits the ground. If the leg stops in a distance of 1.1 cm. Calculate the force on the ankle joint. The mass of the joggers leg is 9.5 kg
stops in .011 meter
average speed during deacceleration = 7.3/2 = 3.65 m/s
so time to stop = .011/3.65 = .00301 second
momentum change = 9.5 * 7.3 = 69.4 kg m/s
so F = d (mv)/dt = 69.4 kg m/s / .00301 s
= 23012 kg m/s^2 or Newtons
Note - I used Newtons original second law which is Force = rate of change of momentum. For constant mass this is F = m a
To calculate the force on the ankle joint, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
In this case, we need to calculate the acceleration first. We can use the equation of motion:
vf^2 = vi^2 + 2aΔx
Where:
vf = final velocity (0 m/s in this case, since the leg stops)
vi = initial velocity (7.3 m/s)
a = acceleration
Δx = displacement (1.1 cm, which is 0.011 m)
Rearrange the equation to solve for acceleration:
a = (vf^2 - vi^2) / (2Δx)
= (0 - (7.3 m/s)^2) / (2 * 0.011 m)
a ≈ -1865.45 m/s^2 (negative sign indicates deceleration)
Now, we can calculate the force:
F = m * a
= 9.5 kg * (-1865.45 m/s^2)
F ≈ -17,717.18 N (negative sign indicates the force is exerted in the opposite direction of motion)
The magnitude of the force, considering it is negative due to deceleration, is approximately 17,717.18 Newtons.
To calculate the force on the ankle joint, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, we need to find the acceleration.
First, let's convert the distance from centimeters to meters:
1.1 cm = 0.011 m
Now, we need to find the deceleration (negative acceleration) of the leg. We can use the following formula to calculate the acceleration:
v^2 = u^2 + 2as
Where:
v is the final velocity (which is 0 m/s since the leg stops)
u is the initial velocity (7.3 m/s)
s is the distance (0.011 m)
Rearranging the formula to solve for the acceleration (a), we have:
a = (v^2 - u^2) / (2s)
Substituting the values, we get:
a = (0^2 - 7.3^2) / (2 * 0.011)
Calculating the acceleration, we find:
a = -183.898 m/s^2
Now that we have the acceleration, we can calculate the force on the ankle joint:
F = m * a
Substituting the values, we have:
F = 9.5 kg * (-183.898 m/s^2)
Calculating the force, we find:
F ≈ -1,746.03 N
Therefore, the force on the ankle joint is approximately -1,746.03 Newtons. The negative sign indicates that the force is acting in the opposite direction of motion (deceleration).