Question

1) a. consider a ball of m= 0.50kg. does it take the same amount of additional energy to vertically lift it from 25cm to 30cm as it does to lift from 30cm to 35 cm? if not, which takes more. Why?

b. does it take the same amount of additional energy to speed your car (mass m=1000 kg) up from 25m/s to 30m/s as it does to speed it up from 30m/s to 35m/s? if not which takes more? Why?

c. consider a spring with k=10N/m. Does it take the same amount of additional energy to stretch the spring from 25cm to 30 cm as it does to stretch it from 30cm to 35 cm? If not, Which takes more? why?

Please explain each part thanks!.

Answer 1

I takes same amount of additional energy for both the cases

as additional energy required to lift the ball of mass m from a height h1 to height h2 = mg(h2-h1)

here we have the height difference h2-h1 = 5 cm in both the cases so the additional energy is also same for both cases.

b) Additional energy required for speeding up a mass m from velocity v1 to velocity v2 is given by 0.5*m*(V2^2 - V1^2)

Here for V1 = 25 m/s , V2 = 30 m/s , m = 1000 Kg

Additional energy = 0.5*1000*(30^2 - 25^2) = 137500 J

For the second case

Here for V1 = 30 m/s , V2 = 35 m/s , m = 1000 Kg

Additional energy = 0.5*1000*(35^2 - 30^2) = 162500 J

SO it takes more additional for increasing the velocity from 30 m/s to 35 m/s

c) Additional energy required to stretch the spring from length x1 to x2 cm is given by 0.5*K(x2^2 - x1^2)

Here for x1 = 25 cm = 0.25 m , x2 = 30 cm = 0.3 m , K = 10 N/m

Additional energy = 0.5*10*(0.30^2 - 0.25^2) = 0.1375 J

For the second case

Here for x1 = 30 cm = 0.3 m , V2 = 35 cm = 0.35 m , K = 10 N/m

Additional energy = 0.5*10*(0.35^2 - 0.30^2) =0.1625 J

SO it takes more additional for increasing thelength from 30 cm to 35 cm .