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3 years ago

6

What is an example of 'Centre of Gravity'?

1 answer:

Lera25 [3.4K]3 years ago

5 0

Water bottle and a paper towel role

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A block of unknown mass is attached to a spring with a spring constant of 7.00 N/m 2 and undergoes simple harmonic motion with a

KatRina [158]

Answers:

a) $0.80 kg$

b) $2.12 s$

c) $1.093 m/s^{2}$

Explanation:

We have the following data:

$k=7 N/m$ is the spring constant

$A=12.5 cm \frac{1 m}{100 cm}=0.125 m$ is the amplitude of oscillation

$V=32 cm/s=0.32 m/s$ is the velocity of the block when $x=\frac{A}{2}=0.0625 m$

Now let's begin with the answers:

<h3>a) Mass of the block</h3>

We can solve this by the conservation of energy principle:

$U_{o}+K_{o}=U_{f}+K_{f}$ (1)

Where:

$U_{o}=k\frac{A^{2}}{2}$ is the initial potential energy

$K_{o}=0$ is the initial kinetic energy

$U_{f}=k\frac{x^{2}}{2}$ is the final potential energy

$K_{f}=\frac{1}{2} m V^{2}$ is the final kinetic energy

Then:

$k\frac{A^{2}}{2}=k\frac{x^{2}}{2}+\frac{1}{2} m V^{2}$ (2)

Isolating $m$ :

$m=\frac{k(A^{2}-x^{2})}{V^{2}}$ (3)

$m=\frac{7 N/m((0.125 m)^{2}-(0.0625 m)^{2})}{(0.32 m/s)^{2}}$ (4)

$m=0.80 kg$ (5)

<h3>b) Period</h3>

The period $T$ is given by:

$T=2 \pi \sqrt{\frac{m}{k}}$ (6)

Substituting (5) in (6):

$T=2 \pi \sqrt{\frac{0.80 kg}{7 N/m}}$ (7)

$T=2.12 s$ (8)

<h3>c) Maximum acceleration</h3>

The maximum acceleration $a_{max}$ is when the force is maximum $F_{max}$ , as well :

$F_{max}=m.a_{max}=k.x_{max}$ (9)

Being $x_{max}=A$

Hence:

$m.a_{max}=kA$ (10)

Finding $a_{max}$ :

$a_{max}=\frac{kA}{m}$ (11)

$a_{max}=\frac{(7 N/m)(0.125 m)}{0.80 kg}$ (12)

Finally:

$a_{max}=1.093 m/s^{2}$

5 0

3 years ago

6. A ball rolled 125 m from the top of a hill to the bottom of a hill. How long

leva [86]

Time = distance / speed
T = 125/ 5
T = 25 meters per second

7 0

3 years ago

Monochromatic coherent light shines through a pair of slits. If the wavelength of the light is decreased, which of the following

Law Incorporation [45]

Answer:

he correct answers are a, b

Explanation:

In the two-slit interference phenomenon, the expression for interference is

d sin θ= m λ constructive interference

d sin θ = (m + ½) λ destructive interference

in general this phenomenon occurs for small angles, for which we can write

tanθ = y / L

tan te = sin tea / cos tea = sin tea

sin θ = y / La

un

derestimate the first two equations.

Let's do the calculation for constructive interference

d y / L = m λ

the distance between maximum clos is and

y = (me / d) λ

this is the position of each maximum, the distance between two consecutive maximums

y₂-y₁ = (L 2/d) λ - (L 1 / d) λ₁ y₂ -y₁ = L / d λ

examining this equation if the wavelength decreases the value of y also decreases

the same calculation for destructive interference

d y / L = (m + ½) κ

y = [(m + ½) L / d] λ

again when it decreases the decrease the distance

the correct answers are a, b

7 0

3 years ago

I need this fast can you help me o give 12 points

Elanso [62]

Water as it's the highest specific heat capacity
Hope this helps x

7 0

3 years ago

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A 60-kg cheetah reaches a speed of 30 m/s as it chases its prey.What is the kinetic energy of the cheetah?

Rama09 [41]

The answer would be 27,000 Joules because (1/2) m v^2 =30*900 which equals 27,000 J

4 0

3 years ago

Read 2 more answers