The mass is moving by uniformly accelerated motion, with initial velocity
and acceleration
. Its position at time t is given by the following law:
where we take the initial position
since we are only interested in the distance traveled by the mass.
If we put
into the equation, the corresponding time t is the time it takes for the mass to travel this distance:
And the two solutions for the equation are:
--> negative, we can discard it
--> this is the solution to our problem
A: A resource that will always be there, can be replenished by the biogeochemical cycles. B: Can regenerate if they are alive or can be replenished by biochemical cycles if they are non living.
When a gas is heated to become a plasma, the atoms (or the molecules) of the gas become ionised. In the ionisation, the atoms loose electrons from the exterior energy levels and thus heating to achieve a plasma will create free electrons and ionized atoms (or ionized molecules).
A plasma can not contain neutrons, because neutrons together with protons make the nuclei of the atoms. To free the neutrons from the atomn nuclei there would be necessary HUGE temperatures.
Also a plasma does not contain neutral elements (atoms) or (neutral) molecules, but Ionized atoms and/or molecules and free electrons.
Thus the good answer is d)
Explanation:
Elongation of the wire is:
ΔL = F L₀ / (E A)
where F is the force,
L₀ is the initial length,
E is Young's modulus,
and A is the cross sectional area.
ΔL = T (0.5 m) / ((2.0×10¹¹ Pa) (0.02 cm²) (1 m / 100 cm)²)
ΔL = T (1.25×10⁻⁶ m/N)
T = (80,000 N/m) ΔL
Draw a free body diagram of the mass at the bottom of the circle. There are two forces: tension force T pulling up and weight force mg pulling down.
Sum of forces in the centripetal direction:
∑F = ma
T − mg = mv²/r
T − mg = mω²r
T − (15 kg) (9.8 m/s²) = (15 kg) (2 rev/s × 2π rad/rev)² (0.5 m + ΔL)
T − 147 N = (2368.7 N/m) (0.5 m + ΔL)
Substitute:
(80,000 N/m) ΔL − 147 N = (2368.7 N/m) (0.5 m + ΔL)
(80,000 N/m) ΔL − 147 N = 1184.35 N + (2368.7 N/m) ΔL
(797631.3 N/m) ΔL = 1331.35 N
ΔL = 0.00167 m
ΔL = 1.67 mm
