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IgorC [24]
2 years ago
12

Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m).

determine the coordinates of the center of mass (or center of gravity) of this system.

Physics
1 answer:
melamori03 [73]2 years ago
6 0
Refer to the diagram shown below.

The given data is

mass, kg   Coordinates. m
-------------   -----------------
   2               (0, 0)
   2               (2, 0)
   4               (2, 1)

Total mass, M = 2+2+4 = 8kg
Let (x,y) be the coordinates of M.

Then, taking moments about the origin, we obtain
8x = 2*0 + 2*2 + 4*2 = 12
x = 1.5 m

8y = 2*0 + 2*0 + 4*1 = 4
y = 0.5 m

Answer:  (1.5, 0.5) m




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A 20 kg crate initially at rest on a horizontal floor requires a 80 N horizontal force to set it in motion. Find the coefficient
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Answer:

<em>The coefficient of static friction between the crate and the floor is 0.41</em>

Explanation:

<u>Friction Force</u>

When an object is moving and encounters friction in the air or rough surfaces, it loses acceleration and velocity because the friction force opposes motion.

The friction force when an object is moving on a horizontal surface is calculated by:

Fr=\mu N          [1]

Where \mu is the coefficient of static or kinetics friction and N is the normal force.

If no forces other then the weight and the normal are acting upon the y-direction, then the weight and the normal are equal in magnitude:

N = W = m.g

The crate of m=20 Kg has a weight of:

W = 20*9.8

W = 196 N

The normal force is also N=196 N

We can find the coefficient of static friction by solving [1] for \mu:

\displaystyle \mu=\frac{Fr}{N}

The friction force is equal to the minimum force required to start moving the object on the floor, thus Fr=80 N and:

\displaystyle \mu=\frac{80}{196}

\mu=0.41

The coefficient of static friction between the crate and the floor is 0.41

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3 years ago
Sapting Leng You have a string with a mass of 13.7 q. You stretch the string with a force of 8.39 N, giving it a length of 1.87
marshall27 [118]

Answer:

a)  \lambda=0.935\ \textup{m}

b) f=36.19\approx 36\ \textup{Hz}

Explanation:

Given:

String vibrates transversely fourth dynamic, thus n = 4

mass of the string, m = 13.7 g = 13.7 × 10⁻¹³ kg

Tension in the string, T = 8.39 N

Length of the string, L = 1.87 m

a) we know

L= n\frac{\lambda}{2}

where,

\lambda = wavelength

on substituting the values, we get

1.87= 4\times \frac{\lambda}{2}

or

\lambda=0.935\ \textup{m}

b) Speed of the wave (v) in the string is given as:

v =f\lambda

also,

v=\sqrt\frac{T}{(\frac{m}{L})}

equating both the formula for 'v' we get,

f\lambda=\sqrt\frac{T}{(\frac{m}{L})}

on substituting the values, we get

f\times 0.935=\sqrt\frac{8.39}{(\frac{13.7\times 10^{3}}{1.87})}

or

f=\frac{33.84}{0.935}

or

f=36.19\approx 36\ \textup{Hz}

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2 years ago
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