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Pavlova-9 [17]
3 years ago
6

Consider the following mass distribution where the x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 2.5 kg at (

0.0, 3.3) m, and 4.0 kg at (2.8, 0.0) m. Where should a fourth object of 7.1 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m?
Physics
1 answer:
nekit [7.7K]3 years ago
8 0

Answer:  x = -1.6  y= -1.2

Explanation:

By definition the x- and –y coordinates of the center of mass for a discrete set of bodies, are given by the following expressions:

Xi = ∑ mi. xi  / ∑ mi

Yi = ∑ mi. yi  / ∑ mi

In order to the x- and –y coordinates of the center of mass of all the system, be (0, 0),

both num.erators in the Xi, Yi expressions must be equal to 0.

So, replacing by the values, and taking into account that the 5.0 Kg is located in the origin, we can write the following:

Xi = 2.8 . 4 Kg + X4 . 7.1 Kg = 0   → X4 = -1.6

Yi = 3.3 . 2.5 Kg + Y4 . 7.1 Kg = 0  → Y4 = -1.2

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Two racing boats set out from the same dock and speed away at the same constant speed of 104 km/h for half an hour (0.500 h), th
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The blue boat traveled 6.1 km farther west than the green boat

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Since we have two coordinates (X, Y) we use

X(t) = X0 + vx * t

Y(t) = Y0 + vy * t

The dock will be the origin of coordinates so X0 and Y0 will be zero. The X axis will be pointing west and the Y axis south.

The blue boat moves with a direction 24° south of west, so it will have speeds:

vxb = 104 * cos(24) = 95 km/h

vyb = 104 * sin(24) = 42.3 km/h

And the green boat:

vxg = 104 * cos(37.7) = 82.3 km/h

vyg = 104 * sin(37.7) = 63.6 km/h

After half hour the boats will have arrived at positions

Xb = 95 * 0.5 = 47.5 km

Yb = 42.3 * 0.5 = 21.1 km

And

Xg = 82.3 * 0.5 = 41.4 km

Yg = 63.6 * 0.5 = 31.8 km

The difference in positions of the boats

47.5 - 41.4 = 6.1 km

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A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Fr
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Answer:

x = 0.0537 m or 5.37 cm

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Given:

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Here, Pressure 'P' is given by,

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P = kx/A

As P = 101325 Pa

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3 years ago
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