Question

A mass m = 0.7 kg is released from rest at the origin 0. The mass falls under the influence of gravity. When the mass reaches point A, it is a distance x below the origin 0; when the mass reaches point B it is a distance of 6 x below the origin 0. What is vB/vA?

Answer 1

The value of
`(v_(B))/(v_(A))=2`

Step-by-step explanation:

Given that,

Mass = 0.7 kg

Height = 6

We need to calculate the velocity at point A

Using conservation of energy

`-mgh-0=0-(1)/(2)mv_(A)^2`

`-mgx=-(1)/(2)mv_(A)^2`

`v_(A)=√(2gx)`.....(I)

We need to calculate the velocity at point B

Using conservation of energy

`-mgh-0=0-(1)/(2)mv_(B)^2`

`-mg*4x=-(1)/(2)mv_(B)^2`

`v_(B)=√(8gx)`....(II)

We need to calculate the ratio of the velocity at point A and point B

`(v_(B))/(v_(A))=(√(8gx))/(√(2gx))`

`(v_(B))/(v_(A))=2`

Hence, The value of
`(v_(B))/(v_(A))=2`