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ELEN [110]
3 years ago
8

What is the force on a 250 kg elevator that is falling freely at 9.8 m/sec2?​

Physics
2 answers:
Anettt [7]3 years ago
7 0

Answer:

\boxed {\boxed {\sf 2450 \ Newtons }}

Explanation:

The elevator is falling freely and the only force acting on it is weight. So,  calculate the weight.

We can do this by multiplying the mass by the acceleration of gravity.

W=m*g

The mass of the elevator is 250 kilograms and the acceleration of gravity is 9.8 meters per second squared.

m= 250 \ kg \\g= 9.8 \ m/s^2

Substitute the values into the formula.

W= 250 \ kg * 9.8 \ m/s^2

Multiply.

W=2450 \ kg*m/s^2

  • 1 kilogram meter per second squared is equal to 1 Newton
  • So, our answer of 2450 kg*m/s² is equal to 2450 N

W= 2450 \ N

The force of weight on the elevator is <u>2450 Newtons</u>

Viefleur [7K]3 years ago
6 0

Answer:

Since it is falling freely, the only force on it is its weight, w.

w = m × g = 250 kg × 9.8 m/s^2 = 2450 Newton/N

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Generally the equation for Torque Balance is mathematically given by

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A very long insulating cylinder has radius R and carries positive charge distributed throughout its volume. The charge distribut
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2.E(r) = \frac{1}{4\pi \epsilon_0}\frac{\alpha R}{r}

3.The results from part 1 and 2 agree when r = R.

Explanation:

The volume charge density is given as

\rho (r) = \alpha (1-\frac{r}{R})

We will investigate this question in two parts. First r < R, then r > R. We will show that at r = R, the solutions to both parts are equal to each other.

1. Since the cylinder is very long, Gauss’ Law can be applied.

\int {\vec{E}} \, d\vec{a} = \frac{Q_{enc}}{\epsilon_0}

The enclosed charge can be found by integrating the volume charge density over the inner cylinder enclosed by the imaginary Gaussian surface with radius ‘r’. The integration of E-field in the left-hand side of the Gauss’ Law is not needed, since E is constant at the chosen imaginary Gaussian surface, and the area integral is

\int\, da = 2\pi r h

where ‘h’ is the length of the imaginary Gaussian surface.

Q_{enc} = \int\limits^r_0 {\rho(r)h} \, dr = \alpha h \int\limits^r_0 {(1-r/R)} \, dr = \alpha h (r - \frac{r^2}{2R})\left \{ {{r=r} \atop {r=0}} \right. = \alpha h (\frac{2Rr - r^2}{2R})\\E2\pi rh = \alpha h \frac{2Rr - r^2}{2R\epsilon_0}\\E(r) = \alpha \frac{2R - r}{4\pi \epsilon_0 R}\\E(r) = \frac{\alpha}{4\pi \epsilon_0}(2 - \frac{r}{R})

2. For r> R, the total charge of the enclosed cylinder is equal to the total charge of the cylinder. So,

Q_{enc} = \int\limits^R_0 {\rho(r)h} \, dr = \alpha \int\limits^R_0 {(1-r/R)h} \, dr = \alpha h(r - \frac{r^2}{2R})\left \{ {{r=R} \atop {r=0}} \right. = \alpha h(R - \frac{R^2}{2R}) = \alpha h\frac{R}{2} \\E2\pi rh = \frac{\alpha Rh}{2\epsilon_0}\\E(r) = \frac{1}{4\pi \epsilon_0}\frac{\alpha R}{r}

3. At the boundary where r = R:

E(r=R) = \frac{\alpha}{4\pi \epsilon_0}(2 - \frac{r}{R}) = \frac{\alpha}{4\pi \epsilon_0}\\E(r=R) = \frac{1}{4\pi \epsilon_0}\frac{\alpha R}{r} = \frac{\alpha}{4\pi \epsilon_0}

As can be seen from above, two E-field values are equal as predicted.

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