Question

Very large forces are produced in joints when a person jumps from some height to the ground. (a) Calculate the magnitude of the force produced if an 80.0-kg person jumps from a 0.600–m-high ledge and lands stiffly, compressing joint material 1.50 cm as a result. (Be certain to include the weight of the person.) (b) In practice the knees bend almost involuntarily to help extend the distance over which you stop. Calculate the magnitude of the force produced if the stopping distance is 0.300 m. (c) Compare both forces with the weight of the person.Calculate the magnitude of the force produced if an 80.0-kg person jumps from a 0.600–m-high ledge and lands stiffly, compressing joint material 1.50 cm. (Be certain to include the weight of the person.)

A. 9400 N
B. 9800 N
C. 10200 N
D. 10600 N

Answer 1

The magnitude of the force produced when a person jumps from a height and lands stiffly is 9800 N. The force produced when the knees bend and the stopping distance is increased is 9792 N. Both forces are slightly different from the weight of the person.

Step-by-step explanation:

(a) To calculate the magnitude of the force produced when a person jumps from a height and lands stiffly, we need to consider the change in potential energy and the compression of the joint material. The potential energy change is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. The compression of the joint material can be calculated using Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The equation for Hooke's Law is F = kx, where F is the force, k is the spring constant, and x is the displacement.

Using these equations, we can calculate the force:

Force = Weight + Spring Force

The weight of the person is given by the equation Weight = mg, where g is the acceleration due to gravity. The spring force is given by the equation F = kx. By substituting the values into the equations and solving, we find that the magnitude of the force produced is 9800 N.

(b) To calculate the magnitude of the force when the knees bend and the stopping distance is increased, we can use the equation for work: W = Fd, where W is the work, F is the force, and d is the distance. By substituting the values into the equation and solving, we find that the magnitude of the force produced is 9792 N.

(c) Comparing both forces with the weight of the person, we find that the force produced when landing stiffly is slightly greater than the weight of the person, while the force produced when the knees bend is slightly smaller than the weight of the person.