Question

Fish are hung on a spring scale to determine their mass (most fishermen feel no obligation to report the mass truthfully).

(a) What is the force constant (in N/m) of the spring in such a scale if it stretches 7.90 cm for a 11.0 kg load?

  13645.56 N/m

(b) What is the mass (in kg) of a fish that stretches the spring 5.50 cm?

7,66 kg

(c) How far apart (in mm) are the half-kilogram marks on the scale?

  3.6E-3 mm

Part A and C are wrong and I want details.

Answer 1

Solution:-

a)      Calculate the force constant in (N/m) of the spring in such a scale if it stretches 7.90cm for a 11.0kg load?

Using formula, F = Kx

Where, F – Force, like weight (mg)

K – Spring constant

X – Distance

Now we know m and x for the first one and g of course so rearrange the equation to solve fork.

K = f/x:        k = mg/x

K = (11kg)*(9.8m/s²) / 0.0790m

Notice – I convert the length to meter

K = 1364.55 N/m

K = 1365 N/m

b)     Calculate the mass (in kg) of a fish that stretches the spring 5.50cm?

-Now we are given k (from the last equation) and x we are asked for mass just rearrange the equation to solve for m.

F = kx; mg = kx

m = kx/g

m = (1364.55 N/m)*(0.0550m) / (9.8m/s²)

m = 7.6581 kg

m = 7.6 kg

c)      Now we have k (from the first part of the equation) and mass (one half kg) and they ask for distance x.

F = Kx: x = F/k = mg/k

X = (0.5kg)*(9.8m/s²) / 1364.55N/m

X = 0.0035

X = 0.35cm

X = 3.5mm

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