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scZoUnD [109]
2 years ago
5

A cylinder of mass m is free to slide in a vertical tube. The kinetic friction force between the cylinder and the walls of the t

ube has magnitude f. You attach the upper end of a lightweight vertical spring of force constant k to the cap at the top of the tube, and attach the lower end of the spring to the top of the cylinder. Initially the cylinder is at rest and the spring is relaxed. You then release the cylinder. What vertical distance will the cylinder descend before it comes momentarily to rest? Express your answer in terms of the variables m, f, and constants g, k.
Physics
1 answer:
Lapatulllka [165]2 years ago
7 0

Answer:

x = (mg-f)/k

Explanation:

there are three forces acting on cylinder in a tube, (1) force due to spring = -kx (2) force due to friction = f (3) force due to gravity.

we want to calculate an instant when all three forces acting on mass cancel and there is 0 net force  and cylinder momentiraly comes to stop.

let's write it in mathematics.

kx+f-mg=0 (kx is positive because it is upwards and that is how we have setup our coordinate axis in this problem).

solving for x gives.

x = (mg-f)/k.

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Find the energy released when there is a decrease of 0.3kg of material in a nuclear reaction
MrRissso [65]

Answer:

E = 2.7 x 10¹⁶ J

Explanation:

The release of energy associated with the mass can be calculated by Einstein's mass-energy relation, as follows:

E = mc^2

where,

E = Energy Released = ?

m = mass of material reduced = 0.3 kg

c = speed of light = 3 x 10⁸ m/s

Therefore,

E = (0.3\ kg)(3\ x\ 10^8\ m/s)^2

<u>E = 2.7 x 10¹⁶ J</u>

4 0
2 years ago
1. A mass suspended from a spring oscillates vertically with amplitude of 15 cm. At what distance from the equilibrium position
antiseptic1488 [7]

Answer:

The value of the distance is \bf{14.52~cm}.

Explanation:

The velocity of a particle(v) executing SHM is

v = \omega \sqrt{A^{2} - x^{2}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`~(1)

where, \omega is the angular frequency, A is the amplitude of the oscillation and x is the displacement of the particle at any instant of time.

The velocity of the particle will be maximum when the particle will cross its equilibrium position, i.e., x = 0.

The maximum velocity(\bf{v_{m}}) is

v_{m} = \omega A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)

Divide equation (1) by equation(2).

\dfrac{v}{v_{m}} = \dfrac{\sqrt{A^{2} - x^{2}}}{A}~~~~~~~~~~~~~~~~~~~~~~~~~~~(3)

Given, v = 0.25 v_{m} and A = 15~cm. Substitute these values in equation (3).

&& \dfrac{1}{4} = \dfrac{\sqrt{15^{2} - x^{2}}}{15}\\&or,& A = 14.52~cm

6 0
3 years ago
Calculate the rate of heat conduction through a layer of still air that is 1 mm thick, with an area of 1 m, for a temperature of
max2010maxim [7]

Answer:

The rate of heat conduction through the layer of still air is 517.4 W

Explanation:

Given:

Thickness of the still air layer (L) = 1 mm

Area of the still air = 1 m

Temperature of the still air ( T) = 20°C

Thermal conductivity of still air (K) at 20°C = 25.87mW/mK

Rate of heat conduction (Q) = ?

To determine the rate of heat conduction through the still air, we apply the formula below.

Q =\frac{KA(\delta T)}{L}

Q =\frac{25.87*1*20}{1}

Q = 517.4 W

Therefore, the rate of heat conduction through the layer of still air is 517.4 W

6 0
3 years ago
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Many television sets show 25 images, called 'frames, each second. What is the time interval between one
Firlakuza [10]

Answer:

Given,

Frame rate = 25 frames per second

To find,

Time interval between one frame and the next.

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Now,

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To calculate the time interval between one frame and next, we need to divide the time taken to display total number of frames by total number of frames.

So,

Time interval between one frame and next :

= Time taken to display total number of frames / Total frames

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= 0.04 second

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8 0
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Convection occurs when thermal energy is transferred by the movement of
madam [21]

Answer:

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6 0
2 years ago
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