On a horizontal frictionless surface a mass M is attached to two light elastic strings both having length l and both made of the same material. The mass is displaced by a small displacement Δy such that equal tensions T exist in the two strings, as shown in the figure. The mass is released and begins to oscillate back and forth. Assume that the displacement is small enough so that the tensions do not change appreciably. (a) Show that the restoring force on the mass can be given by F = -(2T∆y)/l (for small angles) (b) Derive an expression for the frequency of oscillation.
Answers
Answer:
ω = √(2T / (mL))
Explanation:
(a) Draw a free body diagram of the mass. There are two tension forces, one pulling down and left, the other pulling down and right.
The x-components of the tension forces cancel each other out, so the net force is in the y direction:
∑F = -2T sin θ, where θ is the angle from the horizontal.
For small angles, sin θ ≈ tan θ.
∑F = -2T tan θ
∑F = -2T (Δy / L)
(b) For a spring, the restoring force is F = -kx, and the frequency is ω = √(k/m). (This is derived by solving a second order differential equation.)
In this case, k = 2T/L, so the frequency is:
ω = √((2T/L) / m)
ω = √(2T / (mL))
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Learn more about Newton's First Law here, refer to the link;
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Answers
Answer:
1124923453 electrons
Explanation:
The formula for charge in coulomb ,C =Current in amperes, A * Time in seconds, s
Given in question ;
Charge = 1.6 * 10⁻¹⁹ C
Current = 2.0 nA = 2*e⁻⁹ A
Calculate time in seconds as
1.6 * 10⁻¹⁹ = 2*e⁻⁹ * t
1.6 * 10⁻¹⁹ /2*e⁻⁹ = t
6.48e⁻¹⁶ s = t
So using t=6.48e⁻¹⁶ s and current =2*e⁻⁹ A , the charge will be;
C = 2*e⁻⁹ * 6.48e⁻¹⁶ =1.799e⁻¹⁰ C
But 1 coulomb = 6.25 x 10¹⁸ electrons
so 1.799e⁻¹⁰ C = ?,,,,{ 6.25 x 10¹⁸} *{1.799e⁻¹⁰} = 1124923453.06 electrons
Answers
You don't need it to solve the problem. The answer would be the same
if the blow drier were operating from a 440-V outlet, or any other kind
(just as long as the blow drier is designed to operate on whatever voltage
it was plugged into.)
Power = 750-W = 0.75 kW
Time = 13 minutes = 13/60 of an hour
Energy = (power) x (time) = (0.75 kW) x (13/60 of an hour) = 0.1625 kWh
Cost per unit of energy = $ 0.1 per kWh
Total cost = (energy) x (cost per unit of energy)
Total cost = (0.1625 kWh) x ($ 0.1 per kWh) = $ 0.01625 = 1.625 cents
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The other answer has his significant figures correct, but shows what happens
when you don't carry your units all the way through.
Answers
Answer:
Raindrops are considered damaging to the soil in the following ways:
- If it is too wet or too dry, nutrients in the soil can run off and not make it to the plants' roots, leading to poor growth and overall health.
- over-watering or too much rain can also lead to bacteria, fungus, and mold growth in the soil
- If the average rainfall is much lower or higher than the ideal, it can lead to significant problems, from drowned crops to lower yields.
- The soil can also start to collect bacteria, mold, and fungus, which can then be absorbed by the plant. While this isn’t as common in crops as it is in indoor plants, poor drainage and irrigation systems can lead to these types of growths taking control over your crops.
- raindrops when it is excessive can lead to erosion and leaching of the soil
- soil loss is mostly affected by increasing runoff discharge of rainwater
Cheers!