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Sedaia [141]
3 years ago
11

A spring with spring constant 40 N/m is attached to the ceiling, and a 5.1-cm-diameter, 1.5 kg metal cylinder is attached to its

lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position.
When in equilibrium, what length of the cylinder is submerged?
Physics
1 answer:
Allisa [31]3 years ago
4 0

Answer: 24.5 cm

Explanation:

Given

Force constant of spring, k = 40 N/m

Diameter of spring, d = 5.1 cm = 0.051 m

Mass of cylinder, m = 1.5 kg

Let us assume that the cylinder is hanging in such a way that the circular end is parallel with the water. Also, we assume that the tank water level is not materially affected by the displacement of the cylinder while the cylinder sinks. The water is fresh and as we all know, the density of water is 1000 kg/m³

To solve this, we assume x to be the spring extension and it's equivalent sinking distance(in meters). We then apply the formula,

mg = kx + ρgAx

mg = x(k + ρgA)

x = mg / (k + ρgA), where

A = πd²/4

A = (3.142 * 0.051²)/4

A = 0.0082 / 4

A = 0.00205 m²

x = 1.5 * 9.81 / [40 + (1000 * 9.81 * 0.00205)]

x = 14.715 / (40 + 20.1105)

x = 14.715 / 60.1105

x = 0.245 m

or 24.5 cm of stretch or sinking

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A stone with a weight of 5.30 N is launched vertically from ground level with an initial speed of 23.0 m/s, and the air drag on
frozen [14]

Answer:

a) h=25.7\ m

b) v'=21.8733\ m.s^{-1}

Explanation:

Given:

  • weight of the stone, w=5.3\ N
  • initial velocity of vertical projection, u=23\ m.s^{-1}
  • air drag acting opposite to the motion of the stone, D=0.266\ N

The mass of the stone:

m=\frac{w}{g}

m=\frac{5.3}{9.8}

m=0.5408\ kg

Now the acceleration of the stone opposite of the motion:

D=m.d

where:

d = deceleration

0.266=0.5408\times d

d=0.4918\ m.s^{-2}

<u>In course of going up the net acceleration on the stone will be:</u>

g'=g+d

g'=9.8+0.4918

g'=10.2918\ m.s^{-2}

a)

Now using the equation of motion:

v^2=u^2-2 g'.h

where:

v= final velocity when the stone reaches at the top of the projectile = 0

h = height attained by the stone before starting to fall down

0^2=23^2-2\times 10.2918\times h

h=25.7\ m

b)

during the course of descend from the top height of the projectile:

initial velocity, v=0\ m.s^{-1}

The acceleration will be:

g"=g-d

g"=9.8-0.4918

g"=9.3082\ m.s^{-2}

here the gravity still acts downwards but the drag acceleration acts in the direction opposite to the motion of the stone, now the stone is falling down hence the drag  acts upwards.

Using equation of  motion:

v'^2=v^2+2g".h (+ve acceleration because it acts in the direction of motion)

v'^2=0^2+2\times 9.3082\times 25.7

v'=21.8733\ m.s^{-1}

8 0
3 years ago
A 60 kg person runs up a set of stairs in B-Building 6 meters high, in a time of 8 seconds.
Assoli18 [71]

Answer:

I could be wrong but I think it is 560 W

6 0
3 years ago
HELP PLZZZZZZ
ValentinkaMS [17]

Hi there!

We know that:

U (Potential energy) = mgh

We are given the potential energy, so we can rearrange to solve for h (height):

U/mg = h

g = 9.81 m/s²

m = 30 g ⇒ 0.03 kg

0.062/(0.03 · 9.81) = 0.211 m

8 0
3 years ago
Which type of thermal energy transfer does a wrapping of cotton or plastic reduce the most, conduction, convection, radiation, t
Veseljchak [2.6K]

Answer: Thermal Energy is energy resulting from the motion of particles; It is a form of kinetic energy and is transferred as heat; Thermal Energy Transfer can occur by three methods: Conduction; Convection; Radiation; Conduction. Conduction is the transfer of thermal energy through direct contact between . particles of a substance.

Explanation:

8 0
3 years ago
A shopper walks westward 2.8 meters in the first 5 minutes and then eastward 9.2 meters in the next 10 minutes. What is the shop
Alecsey [184]

Answer:

12m

Explanation:

Given parameters:

Distance walked westward  = 2.8m

Time of travel  = 5min

Distance walked eastward = 9.2m

Time of travel  = 10min

Unknown:

The total shopper's travel distance  = ?

Solution:

Total distance traveled is the sum of the length of path covered by a body. It is a scalar quantity.

 Total distance = distance walked westward + distance walked eastward

  Total distance  = 2.8m + 9.2m  = 12m

6 0
2 years ago
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