Answer: 276 days
Explanation:
This problem can be solved using the Radioactive Half Life Formula:
(1)
Where:
is the final amount of the material
is the initial amount of the material
is the time elapsed
is the half life of polonium-210
Knowing this, let's substitute the values and find
from (1):
(2)
(3)
(4)
Applying natural logarithm in both sides:
(5)
(6)
Clearing
:
(7)
Answer:U(x) = 30x^2 +6x^3
V^2=8.28m/s
Explanation:The law of conservation of energy is given by K1+U1= K2+U2 ...eq 1
Kinetic energy K.E= 1/2 mv^2
Restoring force function F(x)= -60x - 18x^2
But F(x)= -dU/dx
dU(x)=-F(x)dx
Integrating U(x)= -integral F(x)dx + U(0)
Substituting, we get
U(x) = - integral(-60x-18x^2)dx+U(0)
U(x)= 30x^2+6x^3+U(0)
U=0 at x=0
Therefore U(x)= 30x^2+6x^3
b) Given : x1=1.00m,x2= 0.50m ,V1=0, V2=?
Substituting into eq (a)
U1= 30(1.00)^2+6(1.00)^3=36J
Using x2=0.5 into eq(a)
U2=30(0.50)^2+6(0.50)^3=8.25J
Object at rest K1=0
0+36=K2+8.25
K2=27.75J
Given; m =0.900kg, V2=?
27.75=1/2×0.900×V2^2
V2= SQRT(2×27.75)/0.81
V2= 8.28m/s
Answer:
α = π/3
β = π/6
Explanation:
Use arc length equation to find the sum of the angles.
s = rθ
π/20 m = (0.1 m) (α + β)
π/2 = α + β
Draw a free body diagram for each sphere. Both spheres have three forces acting on them:
Weight force mg pulling down,
Normal force N pushing perpendicular to the surface,
and tension force T pulling tangential to the surface.
Sum of forces on A in the tangential direction:
∑F = ma
T − m₁g sin α = 0
T = m₁g sin α
Sum of forces on B in the tangential direction:
∑F = ma
T − m₂g sin β = 0
T = m₂g sin β
Substituting:
m₁g sin α = m₂g sin β
m₁ sin α = m₂ sin β
(1 kg) sin α = (√3 kg) sin (π/2 − α)
1 sin α = √3 cos α
tan α = √3
α = π/3
β = π/6
Answer:
It will travel to the infinity and beyond
Answer:
The work required is -515,872.5 J
Explanation:
Work is defined in physics as the force that is applied to a body to move it from one point to another.
The total work W done on an object to move from one position A to another B is equal to the change in the kinetic energy of the object. That is, work is also defined as the change in the kinetic energy of an object.
Kinetic energy (Ec) depends on the mass and speed of the body. This energy is calculated by the expression:

where kinetic energy is measured in Joules (J), mass in kilograms (kg), and velocity in meters per second (m/s).
The work (W) of this force is equal to the difference between the final value and the initial value of the kinetic energy of the particle:


In this case:
- W=?
- m= 2,145 kg
- v2= 12

- v1= 25

Replacing:

W= -515,872.5 J
<u><em>The work required is -515,872.5 J</em></u>