Question

A basketball is placed on the spring from a car's shock absorber, which has a spring constant of 100,000 n/m. the weight of the basketball only compresses the spring a negligible amount (a fraction of a millimeter). you use your open hand to press down on the ball and compress the spring by an additional 5 mm. estimate the solid pressure (a.k.a, compressive stress) on the surface of your hand. assume the force that you use is applied uniformly across the entire surface of your hand and neglect the any effect from the basketball's curvature. give your answer in units of pascals (pa).

Answer 1

The compressive stress on the surface of your hand when compressing a car's shock absorber spring by an additional 5 mm is approximately 5,000 pascals, computed using Hooke's Law and the pressure formula with a spring constant of 100,000 N/m and an estimated hand contact area of 0.1 m^2.

Step-by-step explanation:

To estimate the compressive stress on the surface of your hand when you compress a car's shock absorber spring with a basketball by an additional 5 mm, you need to first calculate the force exerted by the spring using Hooke's law and then the pressure (or stress) exerted on your hand.

Using Hooke's Law, F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the compression distance. Here, k = 100,000 N/m and x = 5 mm = 0.005 m. Plugging in the values, we get F = 100,000 N/m * 0.005 m = 500 N.

To find the pressure applied to your hand, use the pressure formula P = F/A, where P is the pressure, F is the force, and A is the contact area. Assuming an average hand contact area of about 0.1 m^2, the pressure would be P = 500 N / 0.1 m^2 = 5,000 Pa.