hmm The magnitude of the force that a spring exerts (F) when it is stretched a d

Question

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The magnitude of the force that a spring exerts (F) when it is stretched a distance x from its unstressed length is governed by Hooke's law, F = kx. What are the dimensions of the force constant, k? (Use the following as necessary: M for mass, T for time, and L for length.) k = What are the dimensions and SI units of the quantity kx2? (For the dimension use L for length, M for mass, and T for time. For the units use m for meters, kg for kilograms, and s for seconds.) dimensions SI units Write the following in scientific notation. 1343900 m 12430 kW 55.35 ps 5.0 m

Explanation / Answer

1. Force constant has units of N/m. N has dimensions MLT^(-2). So, k has dimensions MT^2

2. Units of kx^2 = Joule (J). Dimensions = ML^2T^(-2)

1343900m = 1343.9 km = 1.3439 x 10 ^3 km

12430 kW = 1.2430 x 10^1 MW

55.35 ps = 5.535 x 10 ^ (-11)s

5.0 m = 5 x 10^3 mm

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