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yuradex [85]
2 years ago
10

An object with mass of 4kg is thrown with initial velocity of 20m/s from point A and follows the track of ABCD.

Physics
1 answer:
soldier1979 [14.2K]2 years ago
5 0

<u>The distance of the length YD is 3.57m, the velocity of the object at point D is 27m/s and the time required for the object to reach the ground is 0.17s</u>

Data given;

  • Mass = 4kg
  • Initial velocity = 20m/s
  • length CD = 5m (from the image given)

a)

<h3>Determine The Length of YD</h3>

YD=CDsinθ = 5sin45=\frac{5}{\sqrt{2} } = 3.57m

b)

<h3>The velocity of the object at point D</h3>

The change in kinetic energy is given as

Δ in kinetic energy = Δ in potential energy + work done by friction

K.E - 1/2mv^2 = mgh_1 - mgh_2 + (-μmg.x)

K.E = mg(50 - 3.57) + (-mg(0.3*100) + 1/2 mv^2

\frac{1}{2}mv^2_f=mg(46.43)-mg(30)+\frac{1}{2} m(400)\\\\v^2_f=20(16.43)+400\\v^2_f=728.6\\v=\sqrt{728.6} \\v_f=26.99 = 27m/s

The velocity of the object at D with a distance of 5m.

c)

<h3>The the required for the object to reach ground</h3>

The velocity of the object in the y-axis is

v_y=vsin45=19.09

Acceleration in y-axis = 9.8

Height = 3.57m

h = ut+\frac{1}{2}at^2

3.57=19.28(t)+\frac{1}{2}(9.8)t^2\\3.57=19.28t+4.9t^2\\4.9t^2+19.28t-3.57=0\\a=4.9, b=19.28, c= -3.57\\t=\frac{-19.28+\sqrt{(19.28)^2-4(4.9)(-3.57)} }{(2*4.9)} \\t=\frac{-19.28+21.02}{9.8}

Taking the positive value

\frac{-19.28+21.02}{9.8}=0.17s

The time required for the object to reach ground is 0.17s

From the calculations above,<u> the distance YD is 3.57m, the velocity of the object at point D is 27m/s and the time required for the object to reach ground is 0.17s</u>

Learn more on projectile motion here;

brainly.com/question/1130127

<h3 />
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Density of copper is 8.96 g/cm3and density of zinc is 7.14 g/cm3. Brass is an alloy made of copper and zinc. You are given a sam
kvasek [131]

Answer:

The material cost for making one ton of the brass sample that I have is $8149.04.

Explanation:

Density of copper = 8.96 g/cm^3 = 8.96×10^-3 kg/cm^3

Price of copper = $6.13/kg

Price of copper per volume = 8.96×10^-3 kg/cm^3 × $6.13/kg = $0.0549/cm^3

Density of zinc = 7.14 g/cm^3 = 7.14×10^-3 kg/cm^3

Price of zinc = $1.8/kg

Price of zinc per volume = 7.14×10^-3 kg/cm^3 × $1.8/kg = $0.0129/cm^3

Price of brass per volume = 0.0549 + 0.0129 = $0.0678/cm^3

Density of brass I have is 8.32 g/cm^3 = 8.32 g/cm^3 × 1 kg/1000 g × 1 ton/1000 kg = 8.32×10^-6 ton/cm^3

Price = $0.0678/cm^3 ÷ 8.32×10^-6 ton/cm^3 = $8149.04/ton

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3 years ago
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A 4.87-kg ball of clay is thrown downward from a height of 3.21 m with a speed of 5.21 m/s onto a spring with k = 1570 N/m. The
Yuki888 [10]

Answer:

Approximately 0.560\; {\rm m}, assuming that:

  • the height of 3.21\; {\rm m} refers to the distance between the clay and the top of the uncompressed spring.
  • air resistance on the clay sphere is negligible,
  • the gravitational field strength is g = 9.81\; {\rm m\cdot s^{-2}}, and
  • the clay sphere did not deform.

Explanation:

Notations:

  • Let k denote the spring constant of the spring.
  • Let m denote the mass of the clay sphere.
  • Let v denote the initial speed of the spring.
  • Let g denote the gravitational field strength.
  • Let h denote the initial vertical distance between the clay and the top of the uncompressed spring.

Let x denote the maximum compression of the spring- the only unknown quantity in this question.

After being compressed by a displacement of x, the elastic potential energy \text{PE}_{\text{spring}} in this spring would be:

\displaystyle \text{PE}_{\text{spring}} = \frac{1}{2}\, k\, x^{2}.

The initial kinetic energy \text{KE} of the clay sphere was:

\displaystyle \text{KE} = \frac{1}{2}\, m \, v^{2}.

When the spring is at the maximum compression:

  • The clay sphere would be right on top of the spring.
  • The top of the spring would be below the original position (when the spring was uncompressed) by x.
  • The initial position of the clay sphere, however, is above the original position of the top of the spring by h = 3.21\; {\rm m}.

Thus, the initial position of the clay sphere (h = 3.21\; {\rm m} above the top of the uncompressed spring) would be above the max-compression position of the clay sphere by (h + x).

The gravitational potential energy involved would be:

\text{GPE} = m\, g\, (h + x).

No mechanical energy would be lost under the assumptions listed above. Thus:

\text{PE}_\text{spring} = \text{KE} + \text{GPE}.

\displaystyle \frac{1}{2}\, k\, x^{2} = \frac{1}{2}\, m\, v^{2} + m\, g\, (h + x).

Rearrange this equation to obtain a quadratic equation about the only unknown, x:

\displaystyle \frac{1}{2}\, k\, x^{2} - m\, g\, x - \left[\left(\frac{1}{2}\, m\, v^{2}\right)+ (m\, g\, h)\right] = 0.

Substitute in k = 1570\; {\rm N \cdot m^{-1}}, m = 4.87\; {\rm kg}, v = 5.21\; {\rm m\cdot s^{-1}}, g = 9.81\; {\rm m \cdot s^{-2}}, and h = 3.21\; {\rm m}. Let the unit of x be meters.

785\, x^{2} - 47.775\, x - 219.453 \approx 0 (Rounded. The unit of both sides of this equation is joules.)

Solve using the quadratic formula given that x \ge 0:

\begin{aligned}x &\approx \frac{-(-47.775) + \sqrt{(-47.775)^{2} - 4 \times 785 \times (-219.453)}}{2 \times 785} \\ &\approx 0.560\; {\rm m}\end{aligned}.

(The other root is negative and is thus invalid.)

Hence, the maximum compression of this spring would be approximately 0.560\; {\rm m}.

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Answer:

The horizontal component of displacement is d' = 1422.7 m

Explanation:

Given data,

The distance covered by the truck, d = 1430 m

The angle formed with the horizontal, Ф = 5.76°

The displacement is a vector quantity.

The horizontal component of displacement is given by,

                                 d' = d cos Ф

                                     = 1430 cos 5.76°

                                     = 1422.7 m

Hence, the horizontal component of displacement is d' = 1422.7 m

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A particle with charge − 2.74 × 10 − 6 C −2.74×10−6 C is released at rest in a region of constant, uniform electric field. Assum
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Answer:

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Explanation:

We are given that

Charge of particle=q=-2.74\times 10^{-6} C

Kinetic energy of particle=K_E=6.65\times 10^{-10} J

Initial time=t_1=6.36 s

Final potential difference=V_2=0.351 V

We have to find the time t after that the particle is released and traveled through a potential difference 0.351 V.

We know that

qV=K.E

Using the formula

2.74\times 10^{-6}V_1=6.65\times 10^{-10} J

V_1=\frac{6.65\times 10^{-10}}{2.74\times 10^{-6}}=2.43\times 10^{-4} V

Initial voltage=V_1=2.43\times 10^{-4} V

\frac{\initial\;voltage}{final\;voltage}=(\frac{initial\;time}{final\;time})^2

Using the formula

\frac{V_1}{V_2}=(\frac{6.36}{t})^2

\frac{2.43\times 10^{-4}}{0.351}=\frac{(6.36)^2}{t^2}

t^2=\frac{(6.36)^2\times 0.351}{2.43\times 10^{-4}}

t=\sqrt{\frac{(6.36)^2\times 0.351}{2.43\times 10^{-4}}}

t=241.7 s

Hence, after 241.7 s the particle is released has it traveled through a potential difference of 0.351 V.

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