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valina [46]
3 years ago
7

An ideal spring hangs from the ceiling. A 1.55 kg1.55 kg mass is hung from the spring, stretching the spring a distance ????=0.0

855 md=0.0855 m from its original length when it reaches equilibrium. The mass is then lifted up a distance ????=0.0235 mL=0.0235 m from the equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through the equilibrium position?

Physics
1 answer:
Cloud [144]3 years ago
8 0

Answer: 0.048 J

Explanation:

The described situation is better understood with the attached figure.

Let's assume that when the mass is released after being lifted up, it starts performing simple harmonic motion with an amplitude L. Then, the maximum speed V of this hanging mass is fulfilled at the equilibrium position and its given by the following equation:

V=\sqrt{\frac{k}{m}}L (1)

Where:

k is the spring constant which can be calculated by the Hooke's law: k=\frac{F}{d}=\frac{mg}{d} being g=9.8 m/s^{2} the acceleration due gravity and d=0.0855 m the length the spring is streched.

m=1.55 kg is the mass

L=0.0235 m is the amplitude

So, k=\frac{(1.55 kg)(9.8 m/s^{2})}{0.0855 m}=177.66 N/m (2)

Substituting (2) in (1):

V=\sqrt{\frac{177.66 N/m}{1.55 kg}}0.0235 m (3)

V=0.251 m/s (4)

On the other hand, the kinetic energy K is given by the following equation:

K=\frac{1}{2}mV^{2} (5)

K=\frac{1}{2}(1.55 kg)(0.251 m/s)^{2} (6)

Hence:

K=0.048 J

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6 0
3 years ago
Two liquids, A and B, have equal masses and equal initial temperatures. Each is heated for the same length of time over identica
DochEvi [55]

Answer:

So the specific heat of the liquid B is greater than that of A.

Explanation:

Liquid A is hotter than the liquid B after both the liquids are heated identically for the same duration of time from the same initial temperature then according to heat equation,

Q=m.c.\Delta T

where:

m = mass of the body

c = specific heat of the body

\Delta T= change in temperature of the body

The identical heat source supplies the heat for the same amount of time then the quantity of heat supplied is also equal.

So for constant heat, constant mass the temperature change is inversely proportional to the specific of heat of the liquid.

\Delta T=\frac{Q}{m} \times \frac{1}{c}

\Delta T\propto\frac{1}{c}

So the specific heat of the liquid B is greater than that of A.

5 0
3 years ago
Debido al desorden en el laboratorio un científico tiene 2 termómetros diferentes pero no sabe en qué escalas están por lo que d
just olya [345]

Answer:

La escala del termómetro ''A'' es grados Celsius.

La escala del termómetro ''B'' es grados Fahrenheit.

Explanation:

Para hallar en qué escalas están los termómetros partimos de que la mezcla a la cuál se midió su temperatura mantuvo su temperatura constante.

Esto quiere decir que los termómetros están expresando la misma temperatura pero en una escala distinta.

Sabemos que dada una temperatura en grados Celsius ''C'' si la queremos convertir a grados Fahrenheit ''F'' debemos utilizar la siguiente ecuación :

F=(\frac{9}{5})C+32 (I)

Ahora, si reemplazamos y asumimos que la temperatura de 18° es en grados Celsius, entonces si reemplazamos C=18 en la ecuación (I) deberíamos obtener F=64.4 ⇒

F=(\frac{9}{5}).(18)+32=32.4+32=64.4

Efectivamente obtenemos el valor esperado. Finalmente, corroboramos que la temperatura del termómetro ''A'' está medida en grados Celsius y la temperatura del termómetro ''B'' en grados Fahrenheit.

6 0
3 years ago
A 0.0250-kg bullet is accelerated from rest to a speed of 550 m/s in a 3.00-kg rifle. The pain of the rifle’s kick is much worse
kondaur [170]

Answer:

a) 4.583 m/s

b) 31.505 J

c) 0.491 m/s

d) 3.375 J

e)

   p_player = (110 kg)(8 m/s) = 880 kg m/s

   p_ball = (0.41 kg)(25 m/s) = 10.25 kg m/s

Explanation:

HI!

a)

We can calculate the recoil velocity by conservation of momentum, remember that p=mv.

The momentum of the bullet is:

p_b = (0.0250 kg)*(550 m/s )

The momentum of the rifle is:

p_r = (3 kg) * v

Since the total initial momentum is zero:

p_b = p_r

That is:

v = (550 m/s ) (0.0250 kg/ 3 kg ) = 4.583 m/s

b)

The kinetic energy gained by the rifle is:

K = (1/2) m v^2 = (1/2) *(3 kg) *(4.583 m/s)^2 = 31.505 J

c)

We use the same formula as in a), but with m=28kg instead of 3 kg

v = (550 m/s ) (0.0250 kg/ 28 kg ) = 0.491 m/s

d)

Again, the same formula as b, but with m=28 and v=0.491 m/s

K = 3.375 J

e)

p_player = (110 kg)(8 m/s) = 880 kg m/s

p_ball = (0.41 kg)(25 m/s) = 10.25 kg m/s

I believe that the kinetic energy is more related to the problem than the momentum. The relation between these two quantities is:

K = p^2/(2m)

usiing this relation, we get:

K_player = 3520 J

K_ball =  128.125 J

Therefore the kinetic energy of the player is around 27 time larger than the kinetic energy of the ball, that being said, the pain of being tackled by that player is around 27 times greater that being hit by the ball!

4 0
3 years ago
A 35.9 g mass is attached to a horizontal spring with a spring constant of 18.4 N/m and released from rest with an amplitude of
lidiya [134]

Answer:

7.74m/s

Explanation:

Mass = 35.9g = 0.0359kg

A = 39.5cm = 0.395m

K = 18.4N/m

At equilibrium position, there's total conservation of energy.

Total energy = kinetic energy + potential energy

Total Energy = K.E + P.E

½KA² = ½mv² + ½kx²

½KA² = ½(mv² + kx²)

KA² = mv² + kx²

Collect like terms

KA² - Kx² = mv²

K(A² - x²) = mv²

V² = k/m (A² - x²)

V = √(K/m (A² - x²) )

note x = ½A

V = √(k/m (A² - (½A)²)

V = √(k/m (A² - A²/4))

Resolve the fraction between A.

V = √(¾. K/m. A² )

V = √(¾ * (18.4/0.0359)*(0.395)²)

V = √(0.75 * 512.53 * 0.156)

V = √(59.966)

V = 7.74m/s

8 0
3 years ago
Read 2 more answers
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