Use the conservation of angular momentum; angular momentum at the beginning = angular momentum at the end
Conservation of angular momentum:
I1 w1 = I2 w2
Where I is the moment of inertia. For a sphere, I=2/5 m R^2. Substituting into the equation above we get
w2 = I1 w1 / I2 = w1 m1 R1^2 / (m2 R2^2)
w2 = w1 4 * (R1/R2)^2
= 4*(1)*(7E5/7.5)^2
= 3.48E10 revs/(17days)
= 2.04705882 x 10^9 revs/sec

4 0

3 years ago

A single conservative force acts on a 5.30-kg particle within a system due to its interaction with the rest of the system. The e

cupoosta [38]

Answer:

Given that

m = 5.3 kg

Fx = 2x + 4

We know that work done by force F given as

w= ∫ F. dx

Given that x=1.08 m to x=6.5 m

Fx = 2x + 4

w= ∫ F. dx

$w=\int_{1.08}^{6.5}(2x+4) .dx$

$w=\left [x^2+4x \right ]_{1.08}^{6.5}$

$w=(6.5^2-1.08^2)+4(6.5-1.08)\ J$

w=62.7 J

We know that potential energy given as

$F=-\dfrac{dU}{dx}$

∫ dU = -∫F.dx ( w= ∫ F. dx)

ΔU= -62.7 J

We know that form work power energy theorem

Net work = Change in kinetic energy

W= KE₂ - KE₁

62.7 =KE₂ - (1/2)x 5.3 x 3²

KE₂ = 86.55 J

This is the kinetic energy at 6.5m

8 0

3 years ago

A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling

solniwko [45]

Answer:

17.86 m

Explanation:

The first step is to find the velocity of the swimmer.

Velocity, v = s/t

Velocity, v = 5 / 0.27

Velocity, v = 18.52 m/s

Then, we find the height

h = ½gt²

h = ½ * 9.8 * 0.27²

h = 4.9 * 0.0729

h = 0.36 m

Next, we apply the law of conservation of energy

mgH = mgh + ½ mv²

9.8Hm = m(9.8 * 0.36 + 0.5 * 18.52²)

9.8H = 3.528 + 171.4952

9.8H = 175.02

H = 175.02 / 9.8

H = 17.86 m

Therefore, the needed height is 17.86 m

8 0

4 years ago