Ask question

Ask question

All categories

4 years ago

7

The ball's gravitational potential energy as a function of its height after release. The ball's kinetic energy as a function of

its height after release. The ball's total mechanical energy as a function of its height after release.

1 answer:

zaharov [31]4 years ago

5 0

Answer:

a) U = - G m₁m₂ / r , b) K = ½ m (v₀² + 2gy)² or K = 2 mg² y² c) Em = m g y (2 g y + 1)

Explanation:

Let's write the functions that are requested

a) Gravitational power energy

U = - dF / dr

F = G m₁ m₂ / r²

U = - G m₁m₂ / r

r is the height

b) The scientific enrgia

K = ½ m v²

Cinematic

v² = v₀² + 2 g y

K = ½ m (v₀² + 2gy)²

If the initial velocity is zero, the ball is released

K = ½ m 4 g² y²

K = 2 mg² y²

c) Mechanical energy

Em = K + U

Em = 2 m g² y² + m g y

Em = m g y (2 g y + 1)

You might be interested in

In an oscillating series RLCcircuit, with a 6.13 Ω resistor and a 15.2 H inductor, find the time required for the maximum energy

ivanzaharov [21]

Answer:

time for maximum energy is 1.718 sec

Explanation:

Maximum energy on the capacitor is given as $=\frac{q_{max}^2}{ 2C}$

Maximum energy $= \frac{(1/6) Q_2}{2C}$

The maximum charge is given by

$q_{max} =Qe^{-Rt/2L}$

Or $\frac{q_{max}}{Q} = e^{-Rt/2L}$

Or $ln\frac{q_{max}}{Q} = \frac{-Rt}{2L}$

solving for t

$t = \frac{2L}{R}\frac{1}{2} ln( 2)$

Putting all value to get desired value

$t = ln(2)\times \frac{L}{R}$

$t = 0.693\times \frac{(15.2}{6.13} = 1.71 sec$

8 0

3 years ago

How far does light travel in 13 s?

Zolol [24]

Answer:

2,421,666 miles

Explanation:

light travels 186,282 miles per second in a vaccum.

So 186,282 × 13 = 2,421,666

4 0

4 years ago

Gayle runs at a speed of 3.85 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After s

enot [183]

Answer:

Final velocity at the bottom of hill is 15.56 m/s.

Explanation:

The given problem can be divided into four parts:

1. Use conservation of momentum to determine the speed of the combined mass (Gayle and sled)

From the law of conservation of momentum (perfectly inelastic collision), the combined velocity is given as:

$p_i = p_f$

$m_1u_1 + m_2v_2 = (m_1 + m_2)v$

$v = \frac{(m_1u_1 + m_2v_2)}{(m_1 + m_2)}$

$v=\frac{[50.0\ kg)(3.85\ m/s) + 0]}{(50.0\ kg + 5.00\ kg)}= 3.5\ m/s$

2. Use conservation of energy to determine the speed after traveling a vertical height of 5 m.

The velocity of Gayle and sled at the instant her brother jumps on is found from the law of conservation of energy:

$E(i) = E(f)$

$KE(i) + PE(i) = KE(f) + PE(f)$

$0.5mv^2(i) + mgh(i) = 0.5mv^2(f) + mgh(f)$

$v(f) = \sqrt{[v^2(i) + 2g(h(i) - h(f))]}$

Here, initial velocity is the final velocity from the first stage. Therefore:

$v(f) = \sqrt{[(3.5)^2+2(9.8)(5.00-0)]}= 10.5\ m/s$

3. Use conservation of momentum to find the combined speed of Gayle and her brother.

Given:

Initial velocity of Gayle and sled is, $u_1(i)=10.5$ m/s

Initial velocity of her brother is, $u_2(i)=0$ m/s

Mass of Gayle and sled is, $m_1=55.0$ kg

Mass of her brother is, $m_2=30.0$ kg

Final combined velocity is given as:

$v(f) = \frac{[m_1u_1(i) + m_2u_2(i)]}{(m_1 + m_2)}$

$v(f)=\frac{[(55.0)(10.5) + 0]}{(55.0+30.0)}= 6.79$ m/s

4. Finally, use conservation of energy to determine the final speed at the bottom of the hill.

Using conservation of energy, the final velocity at the bottom of the hill is:

$E(i) = E(f)$

$KE(i) + PE(i) = KE(f) + PE(f)$

$0.5mv^2(i) + mgh(i) = 0.5mv^2(f) + mgh(f)$

$v(f) = \sqrt{[v^2(i) + 2g(h(i) - h(f))]} \\v(f)=\sqrt{[(6.79)^2 + 2(9.8)(15 - 5.00)]}\\v(f)= 15.56\ m/s$

6 0

3 years ago

Russian ice skater, Alina Zagitova, spins her way to projected Gold in the 2018 Olympics. During one particular spin, she moves

solniwko [45]

By conservation of angular momentum

I1*ω1 = I2*ω2 -----> I1*ω1/I2 = 129*95/32 = 383 RPM <<<<<

383 rev/min * 2πrad/rev * 1min/60s = 383*2π/60 = 40.1 radians/s <<<

3 0

3 years ago

A 3.0 kg rifle is held firmly by a 50.0 kg woman, initially standing still. A 0.06 kg bullet leaves the rifle muzzle with a velo

ohaa [14]

Answer:

48kg

Explanation:

i could be wrong if i am srry

7 0

3 years ago