A 25 kg child is sitting at the top of a 4 m tall slide, what is his potential energy?

How many normal modes of oscillation or natural frequencies does each if the following have: (

Vadim26 [7]

<span>Each of these systems has exactly one degree of freedom and hence only one natural frequency obtained by solving the differential equation describing the respective motions. For the case of the simple pendulum of length L the governing differential equation is d^2x/dt^2 = - gx/L with the natural frequency f = 1/(2π) √(g/L). For the mass-spring system the governing differential equation is m d^2x/dt^2 = - kx (k is the spring constant) with the natural frequency ω = √(k/m). Note that the normal modes are also called resonant modes; the Wikipedia article below solves the problem for a system of two masses and two springs to obtain two normal modes of oscillation.</span>

6 0

3 years ago

A bowling ball is launched from the top of a building at an angle of 35° above the horizontal with an initial speed of 15 m/s. T

Mamont248 [21]

Let $y_0$ be the height of the building and thus the initial height of the ball. The ball's altitude at time $t$ is given by

$y=y_0+\left(15\dfrac{\rm m}{\rm s}\right)\sin35^\circ\,t-\dfrac g2t^2$

where $g=9.80\frac{\rm m}{\mathrm s^2}$ is the acceleration due to gravity.

The ball reaches the ground when $y=0$ after $t=2.9\,\mathrm s$ . Solve for $y_0$ :

$0=y_0+\left(15\dfrac{\rm m}{\rm s}\right)\sin35^\circ(2.9\,\mathrm s)-\dfrac12\left(9.80\dfrac{\rm m}{\mathrm s^2}\right)(2.9\,\mathrm s)^2$

$\implies y_0\approx16.258\,\mathrm m$

so the building is about 16 m tall (keeping track of significant digits).

3 0

3 years ago

Why is cheese only strechy when its hot not when its cold (i spelt stretchy wrong but i dont want to change it cuz that would ta

IgorC [24]

That is a really good question, cheese is stretchy when it is hot is because when you heat it up, it liquefies which makes it stretch. it doesn't stretch when it is cold because it is a solid and solids usually do not stretch.

8 0

3 years ago

A wire with a resistance R is lengthened to 3.07 times its original length by pulling it through a small hole. Find the new resi

charle [14.2K]

Explanation:

Below is an attachment containing the solution.

4 0

3 years ago

A proposed communication satellite would revolve around the earth in a circular orbit in the equatorial plane at a height of 358

aleksandr82 [10.1K]

Answer:

Period is 86811.5 seconds.

Explanation:

${ \boxed{ \bf{T {}^{2} = (\frac{4 {\pi}^{2} }{GM}) {r}^{3} }}}$

${ \tt{T {}^{2} = \frac{4 {(3.14)}^{2} }{(6.6 \times {10}^{ - 11} ) \times (5.98 \times {10}^{24} )} \times {((35880\times {10}^{3}) } + (6370 \times {10}^{3} )) {}^{3} }} \\ \\ { \tt{T {}^{2} = 7.54 \times {10}^{9} }} \\ { \tt{T = \sqrt{7.54 \times {10}^{9} } }} \\ { \tt{T = 86811.5 \: seconds}}$

6 0

3 years ago