This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — b) Step 1: Identify the given values. Natural length, L_0 = 2 cm. Extended length, L = 3.5 cm. Applied force, F = 5 N. Step 2: Calculate the extension (e). The extension is the difference between the extended length and the natural length. e = L - L_0 e = 3.5 cm - 2 cm e = 1.5 cm Convert the extension to meters: e = 1.5 cm × 1 m100 cm = 0.015 m Step 3: Apply Hooke's Law to determine the spring constant (k). Hooke's Law states F = ke. Rearranging for k: k = (F)/(e) k = 5 N0.015 m k = 333.33 N/m The spring constant is 333.33 N/m. d) Step 1: Define impulse. Impulse (I) is defined as the change in momentum ( p) of an object. I = p Step 2: Relate force to momentum using Newton's Second Law. Newton's Second Law states that the net force (F) acting on an object is equal to the rate of change of its momentum. F = ( p)/( t) where t is the time interval over which the force acts. Step 3: Show that impulse can be expressed as F t. From Newton's Second Law, we can rearrange the equation to solve for the change in momentum: p = F t Since impulse I = p, we can substitute to show: I = F t This demonstrates that the impulse on an object can be expressed as the product of the force applied and the time interval over which it acts. All done! What's next?