A 70 kg man jumps 1.00m down onto a concrete walkway. His downward motion stops in .02 seconds. If he forgets to bend his knees, what force is transmitted to his leg bones?
30 n
To calculate the force transmitted to the man's leg bones, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), or F = m * a.
Given that the man's mass (m) is 70 kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we first need to calculate the acceleration (a) experienced by the man when he lands on the concrete walkway.
When the man jumps downward, he will experience an acceleration due to gravity in the opposite direction, which can be calculated using the equation a = g.
Therefore, a = -9.8 m/s^2 (downward direction).
Next, we need to calculate the change in velocity (Δv) experienced by the man when he lands. This can be determined using the formula Δv = a * t, where t is the time taken for the downward motion to stop.
Given that the time (t) is 0.02 seconds, the change in velocity (Δv) is calculated as follows:
Δv = -9.8 m/s^2 * 0.02 s
Δv = -0.196 m/s
Since the man was initially at rest, his final velocity (vf) after landing will be the change in velocity (Δv).
Now, to calculate the force (F) transmitted to the man's leg bones, we can use the formula F = m * Δv.
F = 70 kg * (-0.196 m/s)
F ≈ -13.72 N
Therefore, the force transmitted to the man's leg bones is approximately -13.72 Newtons. The negative sign indicates that the force is in the opposite direction of the man's motion.
To determine the force transmitted to the man's leg bones, we need to use the concept of impulse. Impulse is calculated by multiplying the force exerted on an object by the time over which the force acts. In this case, the downward force acting on the man when he hits the concrete walkway will be equal to his weight, which is given by the formula:
Weight = mass × gravity
Given that the man's mass is 70 kg and the acceleration due to gravity is approximately 9.8 m/s², we get:
Weight = 70 kg × 9.8 m/s² = 686 N
Now, we need to calculate the impulse acting on the man's leg bones. Impulse is given by the formula:
Impulse = force × time
The time of impact is given as 0.02 seconds. Substituting these values, we get:
Impulse = 686 N × 0.02 s = 13.72 N·s
Since the time of impact is very short, we can assume the force exerted on the man's leg bones is approximately equal to the impulse. Hence, the force transmitted to his leg bones is approximately 13.72 Newtons.
Note: This calculation assumes the force is evenly distributed across both leg bones and neglects any other factors that may affect the force distribution, such as muscle strength and flexibility.