Derive the algebraic expression for F and J , then solve for F and J THE PROBLEM

Question

Derive the algebraic expression for F and J , then solve for F and J THE PROBLEM Scientists sometimes need to extract tissue samples from wild animals, such as whales or lions. To minimize impact on the animal, a dart gun is often used and the animal never needs to be captured. Suppose a particular dart having mass m-8.7 g penetrates d-2 cm into the animal, and the dart takes t-88 ms to come to rest within the animal's tissue. The dart's deceleration is constant as it goes into the animal. (a) What is the magnitude of the force felt by the animal? (b) What is the magnitude of the impulse on the animal? PAPER SOLUTION INTERPRET DEVELOP Derive an algebraic expression for the magnitude of the force. Derive an algebraic expression for the magnitude of the impulse. EVALUATE

Explanation / Answer

given -

m = 8.7 g = 8.7x10^-3 kg

d = 2 cm = 0.02 m

t = 88 ms = 0.088 s.

use following expression to know the acceleration -

v = u + at

=> 0 = u + a*0.088

=> u = -a*0.088

and -

v^2 = u^2 + 2*a*s

=> 0 = u^2 + 2*a*0.02

=> 0 = (-a*0.088)^2 + 0.04*a

=> 0.04*a + a^2*0.088^2 = 0

=> a = 0, -0.04 / 0.088^2 = 0, -5.16 m/s^2

you can discard the first value which is 0

so , a = 5.16 m/s^2

(a) F = m*a = 8.7x10^-3 x 5.16 = 0.045 N

(b) Impulse = F*t = 0.045 x 0.088 = 3.95 x 10^-3 N.s.

Expression for force = F = m*a

And expression for Impulse = F*t = m*a*t.

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