Question

The force required to stretch a spring varies directly with the amount the spring is stretched. A spring stretches by 33 m when a 19 N weight is hung from it and the weight is at rest (at equilibrium). The 19 N weight is replaced by an unknown weight W so that the spring is stetched to a new equilibrium position, 17 m below the position if no weight were attached. The weight W is then displaced from equilibrium and released so that it oscillates.

Answer 1

The force required to stretch a spring is directly proportional to the amount the spring is stretched. The force constant can be calculated using the equation F = kx. By substituting the given values into the equation, we can find the unknown weight W.

Step-by-step explanation:

The force required to stretch a spring is directly proportional to the amount the spring is stretched. This can be represented by the equation F = kx, where F is the force, k is the force constant, and x is the amount the spring is stretched. In this scenario, we are given that a 19 N weight stretches the spring by 33 m at equilibrium.

To find the force constant, we can use the equation:

k = F / x = 19 N / 33 m = 0.58 N/m

Next, we need to find the unknown weight W that will stretch the spring to a new equilibrium position 17 m below the position with no weight attached. Using the force constant we calculated, we can use the equation F = kx to find the force required:

F = kx = (0.58 N/m)(17 m) = 9.86 N

Therefore, the unknown weight W that will stretch the spring to the new equilibrium position is 9.86 N.

Answer 2

The period is
`T = 8.27 \ sec`

Step-by-step explanation:

From the question we are told that

The extension of the spring is
`e_1 = 33 \ m`

The first weight applied is
`F_1 = 19 N`

The second weight applied is
`F_2 = W`

The second extension is
`e_2 = 17 \ m`

The spring constant of the spring is mathematically evaluated as

`k = (F_1)/(e_1 )`

substituting values

`k = (19)/(33 )`

`k = 0.576`

We are told that

19 N extended the spring to 33 m

Then W N will extended it by 17 m

Therefore
`W = (19 * 17)/(33)`

`W = 9.788 \ N`

Generally the period of the oscillation is mathematically represented as

`T = 2 \pi \sqrt{(M)/(K) }`

where M is the mass of the W which is mathematically evaluated as

`M = (9.788)/(9.8)`

`M = 1.0 \ kg`

substituting values

`T = 2 \pi \sqrt{(1)/(0.576) }`

`T = 8.27 \ sec`