Question

In testing a new material for shielding spacecraft 145 small ball bearings, each moving at a supersonic speed of 399.5 m/s, collide headon and elastically with the material during a 0.808 min interval. If the bearings each have a mass of 6.1 g and the area of the tested material is 0.78 m2 , what pressure is exerted on the material

Answer 1

Answer:

Pressure, P = 18.68 pascals

Explanation:

Number of ball bearings, n = 145

Initial speed of ball bearings, u = 399.5 m/s

As the ball bearings collide head on and elastically. So,

Final speed of the ball bearings, v = -399.5 m/s

Mass of the ball bearing, m = 6.1 g

Time, t = 0.808 min = 48.48 s

We need to find the the pressure exerted on the material. Let it is equal to P. Mathematically, it is given by :

$P=\dfrac{F}{A}$

Since, F = ma and $a=\dfrac{v-u}{t}$

$P=\dfrac{m(v-u)}{tA}$

For n number of ball bearings.

$P=\dfrac{mn(v-u)}{tA}$

$P=\dfrac{6.1\times 10^{-3}\times 145\times (399.5-(-399.5))}{48.48\times 0.78}$

P = 18.68 pascals

So, the pressure exerted on the material is 18.68 pascals. Hence, this is the required solution.