THE PROBLEM Scientists sometimes need to extract tissue samples from wild animal
ID: 1775157 • Letter: T
Question
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=8.1 g penetrates d=5 cm into the animal, and the dart takes t-86 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 Identify all of the true statements. A. The dart's energy is conserved. B. Standard kinematics equations from Chapter 2 can be applied to the dart. C. Newton's second law can be applied to the dart. D. The dart's momentum is conserved. E. None of the above. DEVELOP Derive an algebraic expression for the magnitude of the force. Derive an algebraic expression for the magnitude of the impulse. EVALUATE ASSESSExplanation / Answer
(a)
acceleration is,
a = 2d/t2 = 2*5x10-2/(86x10-3)2 = 13.52 m/s2
magnitude of the force is,
F = ma = 8.1x10-3 * 1.352 = 0.1095 N = 1.095X10-1 N = 1.1X10-1 N
(b)
impulse is,
J = F*t = 0.1095*86x10-3 = 9.418x10-3 N.s
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equation for force is,
F = ma = m[2d/t2 ]
Equation for impulse is,
J =F*t = mat = m[2d/t2 ]*t = m[2d/t] = 2md/t
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