Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m3 and a speed of 1.20 m/s. The inter

Answer:   1m, 1m, 2m, 2m, 4m, 4m.

It’s important to remember that the masses attached do not influence the number of oscillations.

Explanation:

To determine the number of oscillations (complete cycles), we can apply the formula n = t / T ……equation 1

The variables that impact the period of a simple pendulum are solely its length and gravitational acceleration. The period remains unaffected by factors such as mass.

period (T)= 2 x π x √(L/g) ….equation 2

where π = 3.142, L= rope length, and g = 9.8 m/s (gravitational acceleration)

According to the question, the time (t) is 60 seconds.

By merging equations 1 and 2, we obtain  

number of oscillations = time / (2 x π x √(L/g))

Case 1: for L = 4m

number of oscillations = 60 / ( 2 x 3.142 x √(4/9.8))

= 14.9 = 14 complete cycles (the problem specifies complete cycles)

Case 2: for L = 2m

number of oscillations = 60 / ( 2 x 3.142 x √(2/9.8))

= 21.4 = 21 complete cycles

Case 3: where L = 4m, results in the same as case 1, yielding 14 complete cycles

Case 4: where L = 2m, mirrors the outcome in case 2, producing 21 complete cycles

Case 5: in the instance of L = 1m

number of oscillations = 60 / ( 2 x 3.142 x √(1/9.8))

= 30.1 = 30 complete cycles

Case 6: when L = 1m, which repeats case 5, also gives 30 complete cycles

From these findings, the order of the pendulums from the highest to lowest number of complete cycles is as follows: 1m, 2m, 2m, 4m, 4m.

Remember, the number of oscillations is independent of their respective masses.

Given:
a rod with a circular cross section is experiencing uniaxial tension.
Length, L=1500 mm
radius, r = 10 mm
E=2*10^5 N/mm^2
Force, F=20 kN = 20,000 N
[note: newton (unit) in abbreviation is written in upper case, as in N ]

From the details provided, the cross-section area = π r^2 = 100 π =314 mm^2
(i) Stress,
σ
=F/A
= 20000 N / 314 mm^2
= 6366.2 N/mm^2
= 6370 N/mm^2 (to 3 significant figures)

(ii) Strain
ε
= ratio of extension / original length
= σ / E
= 6366.2 /(2*10^5)
= 0.03183 
= 0.0318 (to three significant figures)

(iii) elongation
= ε * L
= 0.03183*1500 mm
= 47.746 mm
= 47.7 mm  (to three significant figures)

It is stated that, in a typical pulsed-field machine, the magnetic field rises from 0 T to 2.5 T within 200 μs. The change in the magnetic field and time interval are relevant here. The diameter is 2.3 cm, translating to a radius of 0.0115 m. As the magnetic field changes, an induced emf occurs within the ring, determined by: E = 5.19 volts. Thus, the induced emf in the ring equates to 5.19 volts, which is the sought solution.

Density is defined as the mass divided by the volume.

You can alter the density of a substance by adjusting either its mass or volume.

Increasing the volume while maintaining a constant mass will result in a decrease in density (as the denominator of the fraction increases).

Furthermore, reducing the mass while keeping the volume the same will also lower the density (because the numerator is reduced).

Therefore, to achieve a lower density, you should either reduce the mass or increase the volume, keeping the other constant.

I hope this is helpful.

To find the volume, we can utilize the ratio of mass to density, as shown by:

volume = mass / density

 

A. when mass = 5.5 kg = 5500 g; density = 1.60 g/cm^3

volume = 5500 g / (1.60 g/cm^3)

resulting in volume = 3,437.5 cm^3

By rounding according to significant digits:

volume = 3,400 cm^3 = 3.4 L

 

B. when mass = 4.9 kg = 4900 g; density = 1.36 g/cm^3

volume = 4900 g / (1.36 g/cm^3)

calculating gives volume = 3,602.94 cm^3

Considering significant digits:

<span>volume = 3,600 cm^3 = 3.6 L</span>