Blocks with different masses are pushed against a spring one at a time, compress

Question

Blocks with different masses are pushed against a spring one at a time, compressing it different amounts. Each is then launched onto an essentially frictionless horizontal surface that then curves upward, still frictionless (Figure 1) . The table below shows the masses, spring compressions, and maximum vertical height each block achieves.

Mass m (g) : 50.0 , 85.2 , 126 , 50.0 , 85.2

Compression x (cm):2.40 , 3.17 , 5.40 , 4.29 , 1.83

Height h (cm): 10.3 , 11.2 , 19.8 , 35.2 , 3.81

Question: Determine a quantity that, when you plot h against it, should yield a straight line.

A. 4mg/x

B. x^2/2mg

C. x/mg

D. mg/square root of (2x)

What is the answer?

Explanation / Answer

The quantity when we plot h against to it,should be yield a straight line

Consider the quantity as z ,for straight line z and h in the form of

z= ch -----------------------(1)

Here c is constant and it gives the slope of the straight line

Now come to our problem

From the law of conservation of energy

The energy stored in a spring due to compression x= potential energy of the block at a vertical hight h

(1/2) k x2 =m g h --------------(2)

Here k is the spring of force constant and it is constant value

x is the compression in the spring

m is the mass of the block

h vertical height

From (2) we can write

kx2/(2mg)=h

x2/(2mg)=(1/k) h -----------(3)

When we compare above equation (3) with (1) it is clear that it is in the form of straight line

z=(x2/2mg) , c= (1/k)

Therefore the required quantity is x2/2mg

so option B is correct.

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