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patriot [66]
2 years ago
12

the pygmy shrew has an average mass of 2.0 g if 49 of these shrew are placed on a spring scale with a spring constant of 24 N/m

, what is the springs displacement

Physics
1 answer:
olga_2 [115]2 years ago
3 0

Answer:

Spring's displacement, x = -0.04 meters.

Explanation:

Let the spring's displacement be x.

Given the following data;

Mass of each shrew, m = 2.0 g to kilograms = 2/1000 = 0.002 kg

Number of shrews, n = 49

Spring constant, k = 24 N/m

We know that acceleration due to gravity, g is equal to 9.8 m/s².

To find the spring's displacement;

At equilibrium position:

Fnet = Felastic + Fg = 0

But, Felastic = -kx

Total mass, Mt = nm

Fg = -Mt = -nmg

-kx -nmg = 0

Rearranging, we have;

kx = -nmg

Making x the subject of formula, we have;

x = \frac {-nmg}{k}

Substituting into the formula, we have;

x = \frac {-49*0.002*9.8}{24}

x = \frac {-0.9604}{24}

x = -0.04 m

Therefore, the spring's displacement is -0.04 meters.

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Adhira loves to ride her bike around the neighborhood. She starts riding 1.2 miles at 30° S of E. Then, she rides another 2.0 mi
zepelin [54]

Answer:

D = 1.8677 miles , θ = 24.28º at South of West

Explanation:

This is an exercise in adding vectors, the easiest way to solve them is to decompose the vectors and add each component algebraically. Let's use trigonometry

first displacement. d = 1.2 miles to 30º south of East

     cos ( 360-30) = cos (-30) = x₁ / d

     sin (-30) = y₁ / d

     x₁ = d cos (-30)

     y₁ = d sin (-30)

     x₁ = 1.2 cos (-30) = 1,039 miles

     y₁ = 1.2 sin (-30) = -0.6 miles

second shift. d = 2.0 miles to 20º West of South

       cos (270-20) = x₂ / d

       cos (250) = y₂ / d

       x₂ = 2.0 cos 250 = -0.684 miles

       y₂ = 2.0 sin250 = -1.879 miles

Third displacement. d = 1.6 miles to 30º South of West

       cos (180 + 30) = x₃ / d

       sin (210) = y₃ / d

       x₃ = 1.6 cos 210 = -1.3856 miles

       y₃ = 1.6 sin 210 = -0.8 miles

Fourth displacement. d = 2.6 miles to 15º West of North

       cos (90 + 15) = x₄ / d

       sin (105) = y₄ / d

       x₄ = 2.6 cos 105 = -0.6729 miles

       y₄ = 2.6 sin 105 = 2,511 miles

having all the components we add

x-axis  (West-East direction)

       X = x₁ + x₂ + x₃ + x₄

       X = 1.039 -0.684 - 1.3846 - 0.6729

       X = -1.7025 miles

   

       Y = y₁ + y₂ + y₃ + y₄

       Y = -0.6 -1.879 -0.8 +2.511

       Y = -0.768

The modulus of this displacement is we use the Pythagorean theorem

      D = √ (X² + Y²)

      D = √ (1.7025² + 0.768²)

      D = 1.8677 miles

let's use trigonometry to find the direction

       tan θ = Y / X

       θ = tan⁻¹ Y / x

       θ = tan⁻¹ (0.768 / 1.7025)

       θ = 24.28º

as the two components are negative this angle is in the third quadrant

therefore in cardinal direction form is

         θ = 24.28º at South of West

4 0
3 years ago
If someone walkes 1000m <br> in 20min, what is their speed?
slava [35]

Answer:

Distance - 1000m

Time - 20min

Speed - ?

Use the formula of distance ÷ time = speed.

s = d/t

s = 1000m/20min

s = 50 m/min

Hope this helps, thank you !!

6 0
2 years ago
A small wooden block with mass 0.775 kg is suspended from the lower end of a light cord that is 1.50 m long. The block is initia
jeka94

Answer:

34.83 m/s

Explanation:

From the law of conservation of momentum,

initial momentum of bullet = final momentum of block + bullet

mv₀ = (m + M)V

V = mv₀/(m + M)

where m = mass of bullet = 0.0120 kg, v₀ = initial momentum of bullet, M = mass of block = 0.775 kg, V = final velocity of block + bullet.

Now, since the block + bullet rise a height of 0.725 m, from the law of conservation of energy,

potential energy change of block + bullet = kinetic energy change of block + bullet.

So (m + M)gh - 0 = -1/2(m + M)(V₁² - V²) where h = vertical height moved = 0.725 m and V₁ = velocity at 0.725 m and it has zero potential energy initially.

gh = -1/2(V₁² - V²)   (2)

Now, we obtain V₁ from

F = (m + M)V₁²/R since a centripetal force acts on the block + bullet at height 0.725 m. F = tension in chord = 4.88 N and R = length of cord = 1.50 m.

V₁ = √[FR/(m + M)]

Substituting V and V₁ into (2) above, we get

gh = -1/2(FR/(m + M) - [mv₀/(m + M)]²)

-2(m + M)²gh = FR(m + M) - (mv₀)²

v₀ = √([FR(m + M) + 2(m + M)²gh]/m)

substituting the values of the variables into v₀ we have

v₀ = √([4.88 N × 1.50 m × (0.0120 kg + 0.775 kg)  + 2(0.0120 kg + 0.775 kg)² × 9.8 m/s² × 0.725 m]/0.0120 kg)

= √([7.32 × 0.787 + 2(0.787)² × 9.8 m/s² × 0.725 m]/0.0120 kg)

= √(5.76 + 8.80)/0.012 kg

= √14.56/0.012

= √1213.40

= 34.83 m/s

So the initial speed v₀ = 34.83 m/s

7 0
3 years ago
The law of conservation of momentum states that a. the total initial momentum of all objects interacting with one another usuall
dalvyx [7]
According to the Law of conservation of momentum, the total momentum of the system before and after the collision remains same. The momentum may transfer from one object to another as a result of the impact, but the overall momentum of the system remains same.

So, the correct answer is option a.
The total initial momentum of all objects interacting with one another usually equals the total final momentum.
5 0
3 years ago
Read 2 more answers
Suppose that the terminal speed of a particular sky diver is 165 km/h in the spread-eagle position and 320 km/h in the nosedive
coldgirl [10]

Answer:

3.76

Explanation:

We are given that

Terminal speed in the spread -eagle position,v_t=165 km/h

Terminal speed in the nosedive position,v'_t=320km/h

We have to find the ratio of the effective cross-sectional area A in the slower position to that in the faster position.

We  know that

Area, A=\frac{2mg}{C\rho v^2_t}

A_{slower}=\frac{2mg}{C\rho(165)^2}

A_{faster}=\frac{2mg}{C\rho(320)^2}

\frac{A_{slower}}{A_{faster}}=\frac{(320)^2}{(165)^2}

\frac{A_{slower}}{A_{faster}}=3.76

3 0
3 years ago
Read 2 more answers
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