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gregori [183]
3 years ago
7

A ball of mass 0.152 kg is dropped from a height 2.27 m above the ground. The acceleration of gravity is 9.8 m/s 2 . Neglecting

air resistance, determine the speed of the ball when it is at a height 0.903 m above the ground. Answer in units of m/s.
Physics
2 answers:
VMariaS [17]3 years ago
7 0

Answer:

Height to achieve a speed of 2 m/s = 0.20m

Height to achieve a speed of 3 m/s = 0.46m

Height to achieve a speed of 4 m/s = 0.82m

Height to achieve a speed of 5 m/s = 1.28m

Height to achieve a speed of 6 m/s = 1.84m

Natali5045456 [20]3 years ago
5 0

Answer:

8.44 m/s.

Explanation:

Change in Potential Energy = Mass x Acceleration From Gravity x H2 - H1

Kinetic Energy = 1/2 (mass) x [(v2)^2 - v1^2]

g * h = 1/2 * v^2

(9.8) x (2.27) = 1/2 * (v)^2

v^2 = 2[(9.8) x (2.27)]

v = 6.67 m/s

g * delta h = 1/2 * delta v^2

(9.8) x (2.27 - 0.903) = 1/2 * [(v2)^2 - (6.67)^2]

v2^2 = 71.2821

v2 = 8.44 m/s

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A metal has a strength of 414 MPa at its elastic limit and the strain at that point is 0.002. Assume the test specimen is 12.8-m
ser-zykov [4K]

To solve this problem, we will start by defining each of the variables given and proceed to find the modulus of elasticity of the object. We will calculate the deformation per unit of elastic volume and finally we will calculate the net energy of the system. Let's start defining the variables

Yield Strength of the metal specimen

S_{el} = 414Mpa

Yield Strain of the Specimen

\epsilon_{el} = 0.002

Diameter of the test-specimen

d_0 = 12.8mm

Gage length of the Specimen

L_0 = 50mm

Modulus of elasticity

E = \frac{S_{el}}{\epsilon_{el}}

E = \frac{414Mpa}{0.002}

E = 207Gpa

Strain energy per unit volume at the elastic limit is

U'_{el} = \frac{1}{2} S_{el} \cdot \epsilon_{el}

U'_{el} = \frac{1}{2} (414)(0.002)

U'_{el} = 414kN\cdot m/m^3

Considering that the net strain energy of the sample is

U_{el} = U_{el}' \cdot (\text{Volume of sample})

U_{el} =  U_{el}'(\frac{\pi d_0^2}{4})(L_0)

U_{el} = (414)(\frac{\pi*0.0128^2}{4}) (50*10^{-3})

U_{el} = 2.663N\cdot m

Therefore the net strain energy of the sample is 2.663N\codt m

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3 years ago
A 10 g bullet is fired into, and embeds itself in, a 2 kg block attached to a spring with a force constant of 19.6 n/m and whose
dmitriy555 [2]

Answer:

x=0.478\ m is the compression in the spring

Explanation:

Given:

  • mass of the bullet, m=10\ g=0.01\ kg
  • mass of block, M=2\ kg
  • stiffness constant of the spring, k=19.6\ N.m^{-1}
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<u>Now since the bullet-mass gets embed into the block, we apply the conservation of momentum as:</u>

m.u=(M+m).v

0.01\times 300=(2+0.01)\times v

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\rm Kinetic\ energy=Spring\ potential\ energy

\frac{1}{2} (M+m).v^2=\frac{1}{2} k.x^2

\frac{1}{2} \times (2+0.01)\times 1.4925^2=\frac{1}{2} \times 19.6\times x^2

x=0.478\ m is the compression in the spring

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The answer is C. Steer in a straight line while gently slowing down

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Ease up on the accelerator and brake gently.

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