A 70.0-kg man jumps 1.00 m down onto a concrete walkway. His downward motion stops in 0.0400 seconds. If he forgets to bend his knees, what force is transmitted to his leg bones?
A) 15 500 N
B) 7 750 N
C) 4 900 N
D) 3 8740 N
E) 2.600 N
a 15500
To find the force transmitted to the man's leg bones, we can use the equation:
Force = Mass x Acceleration
First, let's find the acceleration experienced by the man. Acceleration is given by the formula:
Acceleration = Change in velocity / Time
Given that the man's downward motion stops in 0.0400 seconds and that he jumps down 1.00 m, we can calculate the change in velocity.
Change in velocity = Final velocity - Initial velocity
Since his downward motion stops, the final velocity is 0 m/s. The initial velocity can be calculated using the equation:
Initial velocity = Square root of (2 x acceleration x distance)
In this case, the distance is 1.00 m. So, we can rearrange the equation as follows:
Initial velocity = Final velocity / Time
Now that we have the initial velocity and the final velocity, we can calculate the change in velocity.
Change in velocity = Final velocity - Initial velocity
Once we have the change in velocity, we can find the acceleration:
Acceleration = Change in velocity / Time
Now that we have the acceleration, we can calculate the force transmitted to the man's leg bones using the equation:
Force = Mass x Acceleration
Given that the man's mass is 70.0 kg, we can substitute the values into the equation to find the force.
Force = 70.0 kg x Acceleration
Now let's calculate the values step by step:
1. Calculate initial velocity:
Initial velocity = Square root of (2 x acceleration x distance)
= Square root of (2 x 9.8 m/s^2 x 1.00 m)
= Square root of (19.6 m^2/s^2)
= 4.43 m/s (rounded to two decimal places)
2. Calculate change in velocity:
Change in velocity = Final velocity - Initial velocity
= 0 m/s - 4.43 m/s
= -4.43 m/s (the negative sign indicates the change in direction)
3. Calculate acceleration:
Acceleration = Change in velocity / Time
= -4.43 m/s / 0.0400 s
= -110.75 m/s^2 (rounded to two decimal places)
4. Calculate force transmitted to the leg bones:
Force = Mass x Acceleration
= 70.0 kg x -110.75 m/s^2
= -7752.5 N (rounded to the nearest whole number)
The force transmitted to the man's leg bones, when he forgets to bend his knees, is approximately -7752.5 N.
However, force is a vector quantity, and the negative sign indicates that the force is in the upward direction. So, the magnitude of the force transmitted to his leg bones is 7752.5 N.
Therefore, the correct answer is B) 7 750 N.