Physics, 31.07.2021 07:20 blackopsty23

Two 51 g blocks are held 30 cm above a table. As shown in the figure, one of them is just touching a 30-long spring. The blocks are released at the same time. The block on the left hits the table at exactly the same instant as the block on the right first comes to an instantaneous rest. What is the spring constant?

Answers: 2

Show answers

Answers

Answer from: zanestone12

The concept of this question can be well understood by listing out the parameters given.

The mass of the block = 51 g = 51 × 10⁻³ kgThe distance of the block from the table = 30 cmLength of the spring = 30 cm

The purpose is to determine the spring constant.

Let us assume that the two blocks are Block A and Block B.

At point A on block A, the initial velocity on the block is zero

i.e. u = 0

We want to determine the time it requires for Block A to reach the table. The can be achieved by using the second equation of motion which can be expressed by using the formula.

$\mathsf{S = ut + \dfrac{1}{2}gt^2}$

From the above formula,

The distance (S) = 30 cm; we need to convert the unit to meter (m).

Since 1 cm = 0.01 mThen, 30cm = 0.3 m

The acceleration (g) due to gravity = 9.8 m/s²

∴

inputting the values into the equation above, we have;

$\mathsf{0.3 = (0)t + \dfrac{1}{2}*(9.80)*(t^2)}$

$\mathsf{0.3 = \dfrac{1}{2}*(9.80)*(t^2)}$

$\mathsf{0.3 =4.9*(t^2)}$

By dividing both sides by 4.9, we have:

$\mathsf{t^2 = \dfrac{0.3}{4.9}}$

$\mathsf{t^2 = 0.0612}$

$\mathsf{t = \sqrt{0.0612}}$

$\mathbf{t =0.247 \ seconds}$

However, block B comes to an instantaneous rest on point C. This is achieved by the dropping of the block on the spring. During this process, the spring is compressed and it bounces back to oscillate in that manner. The required time needed to get to this point C is half the period, this will eventually lead to the bouncing back of the block with another half of the period, thereby completing a movement of one period.

By applying the equation of the time period of a simple harmonic motion.

$\mathbf{T = 2 \pi \sqrt{\dfrac{m}{k}}}$

where the relation between time (t) and period (T) is:

$\mathsf{t = \dfrac{T}{2}}$

T = 2t

T = 2(0.247)

T = 0.494 seconds

$\mathbf{T = 2 \pi \sqrt{\dfrac{m}{k}}}$

By making the spring constant (k) the subject of the formula:

$\mathbf{\dfrac{T}{2 \pi } = \sqrt{ \dfrac{m}{k}}}$

$\Big(\dfrac{T}{2 \pi }\Big)^2 = { \dfrac{m}{k}$

$\dfrac{T^2}{(2 \pi)^2 }= { \dfrac{m}{k}$

$\mathsf{ T^2 *k = 2 \pi^2*m} \\ \\ \mathsf{ k = \dfrac{2 \pi^2*m}{T^2}}$

$\mathsf{ k =\Big( \dfrac{(2 \pi)^2*(51 \times 10^{-3})}{(0.494)^2} \Big) N/m}$

$\mathbf{ k =8.25 \ N/m}$

Therefore, we can conclude that the spring constant between the two 51 g blocks held at a distance 30 cm above a table as a result of instantaneous rest caused by the compression of the spring is 8.25 N/m.

Learn more about simple harmonic motion here:

Two 51 g blocks are held 30 cm above a table. As shown in the figure, one of them is just touching a

Answer from: Quest

watch you tube or play clash royale, mainly clash royale

Answer from: Quest

One splits the atoms and molecules the other combines them

Another question on Physics

Physics, 21.06.2019 19:30

Density of salty water as compared to the density of pure water is(a) is less(b) is always equal(c) is always more(d) may be less or more

Answers: 1

Answer

Physics, 21.06.2019 20:50

Aball is thrown upward in the air, and its height above the ground after t seconds is h ( t ) = 57 t − 16 t 2 feet. find the time t when the ball will be traveling upward at 14.25 feet per second.

Answers: 1

Answer

Physics, 22.06.2019 09:50

Gordon is going for a run through the park, but it is cold outside. the low outside temperature could affect his personal safety.

Answers: 1

Answer

Physics, 22.06.2019 13:30

Select the three ways that the parallel-plate capacitor differs from a car battery.

Answers: 1

Answer

You know the right answer?

Two 51 g blocks are held 30 cm above a table. As shown in the figure, one of them is just touching a...