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Lynna
3 months ago
6

A nonlinear spring is used to launch a toy car. The car is pushed against the spring, compressing the spring 2.5 cm. The force t

he spring exerts on the car is given by the equation F=−Kx2, where K=5000 Nm2. The potential energy stored in the spring when the car is pushed against it is most nearly:________________
Physics
1 answer:
serg [3.5K]3 months ago
5 0

Answer:

1.56 J

Explanation:

According to the data provided,

the spring compression is x = 2.5 cm.

The force exerted by the spring is given by,

F = - k x

where k = 5000 N/m.

We want to find the potential energy stored.

Thus, the energy contained within the spring is

PE = \dfrac{1}{2}kx^2

PE = \dfrac{1}{2}\times 5000\times 0.025^2

PE = 1.56 J

Consequently, the energy stored in the spring amounts to 1.56 J.

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Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller
Softa [3030]

Answer:

σ₁ = 3.167 * 10^{-6} C/m²

σ₂ = 7.6 * 10 ^{-6}  C/m²

Explanation:

Provided Information:

i) Smaller sphere's radius ( r ) = 5 cm.

ii) Larger sphere's radius ( R ) = 12 cm.

iii) Electric field at the larger sphere's surface  ( E₁ ) = 358 kV/m, which is equivalent to 358 * 1000 v/m

E_{1} = (\frac{1}{4\pi\epsilon }) (\frac{Q_{1} }{R^{2} } )

358000 = 9 * 10^{9 } *\frac{Q_{1} }{0.12^{2} }

Charge (Q₁) = 572.8 * 10^{-9} C

Since the electric field inside a conductor is zero, the electric potential ( V ) remains constant.

V = constant

∴\frac{Q_{1} }{R} = \frac{Q_{2} }{r}

Q_{2} = \frac{r}{R} *Q_{1}

Q_{2} = \frac{5}{12} *572.8*10^{-9}   = 238.666 *10^{-9} C

Surface charge density ( σ₁ ) for the larger sphere.

Calculated Area ( A₁ )  = 4 * π * R²  = 4 * 3.14 * 0.12 = 0.180864 m².

σ₁  = \frac{Q_{1} }{A_{1} } = \frac{572.8 *10^{-9} }{0.180864} = 3.167 * 10^{-6}  C/m².

Surface charge density ( σ₂ ) for the smaller sphere.

Calculated Area ( A₂ )  = 4 * π * r²  = 4 * 3.14 * 0.05²  = 0.0314 m².

σ₂ =\frac{Q_{2} }{A_{2} } = \frac{238.66 *10^{-9} }{0.0314} = 7.6 * 10 ^{-6} C/m²

8 0
3 months ago
A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 245 Hz. A person on the pl
Keith_Richards [3271]
through the Doppler effect. The formula for apparent frequency is derived as F apparent = F real x (Vair ± Vobserver) / (Vair ± Vsource). In this scenario, should the observer move towards the source—place a positive sign in the numerator and a negative in the denominator. Since the observer approaches the wall, we apply the formula to derive the necessary speed.
4 0
2 months ago
A person who climbs up something (e.g., a hill, a ladder, the stairs) from the ground gains potential energy. a person's weight
kicyunya [3294]

The following values have been provided:

weight w = 240 lb = 1,067.52 N

energy E = 3,000 J

 

The equation for potential energy is:

E = w h

where h indicates the height that the person needs to ascend, therefore:

h = 3000 / 1067.52

h = 2.81 m

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<span>
</span>

<span>Thus, he must ascend 2.81 meters</span>

3 0
2 months ago
The newly formed xenon nucleus is left in an excited state. Thus, when it decays to a state of lower energy a gamma ray is emitt
ValentinkaMS [3465]

Answer:3.87*10^-4

Explanation:

To determine the mass reduction, delta mass Xe, of the xenon nucleus due to its decay, we first use the provided wavelength of the gamma radiation to calculate its frequency via c = freq*wavelength.

From C=f*lambda we set up: 3*10^8=f*3.44*10^-12.

Solving gives frequency F=0.87*10^20 Hz.

Next, we calculate the emitted energy using the equation E=hf, which translates to E=f*Planck's constant.

Thus, E=0.87*10^20*6.62*10^-34, resulting in E=575.94*10^(-16).

This energy is then converted from joules to MeV.

Utilizing the formula E=mc^2, with c^2 = 931.5 MeV/u, enables us to find the reduction in mass, yielding

3.87*10^-4 u.

6 0
2 months ago
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