A girl swings a 0.250 kg rock attached to a taut string in a circle around her head. Her hand holds the end of the string above her head, and the string angles down slightly (11.9° below the horizontal.). The string is massless and 0.75m long.

A coordinate system lies with its origin a the location where the string comes out of the girl's hand. The positive z-axis points vertically. the projection onto the horizontal plane is such that the string makes an angle of 34.6° with the x-axis.

At a certain instant, the rock makes 2.50 revolutions per second (rev/s) in a counterclockwise direction as seen from above.

What is the tangential velocity vector at this instant?

Question

odell.renner · Accepted Answer

Complete Question

The diagram of with this question is shown on the first uploaded image

Answer:

The value is [tex]v = -6.543 \^ i + 9.47 \^ j + 0 \^ k[/tex]

Explanation:

From the question we are told that

The mass of the rock is [tex]m = 0.250 \ kg[/tex]

The length of the string is [tex]L = 0.75 \ m[/tex]

The angle the string makes horizontal is [tex]\theta = 11.9^o[/tex]

The angle which the projection of the string onto the xy -plane makes with the positive x-axis is [tex]\phi = 34.6^o[/tex]

The angular velocity of the rock is [tex]w = 2.50 rev/s = 2.50 * 2\pi =15.7 \ rad/s[/tex]

Generally the radius of the circle made by the length of the string is mathematically represented as

[tex]r = L cos(\theta )[/tex]

=> [tex]r = 0.75 cos(11.9 )[/tex]

=> [tex]r = 0.734 \ m[/tex]

Generally the resultant tangential velocity is mathematically represented as

[tex]v__{R}} = w * r[/tex]

=> [tex]v__{R}} = 15.7 *0.734[/tex]

=> [tex]v__{R}} = 11.5 \ m/s[/tex]

Generally the tangential velocity along the x-axis is

[tex]v_x = -v__{R}} * sin(\phi)[/tex]

=> [tex]v_x =- 11.5 * sin(34.6)[/tex]

=> [tex]v_x = -6.543 \ m/s[/tex]

The negative sign show that the velocity is directed toward the negative x-axis

Generally the tangential velocity along the y-axis is

[tex]v_y = v__{R}} * cos(\phi)[/tex]

=> [tex]v_y = 11.5 * cos(34.6)[/tex]

=> [tex]v_y = 9.47 \ m/s[/tex]

Generally the tangential velocity along the y-axis is

[tex]v_z = v__{R}} * cos(90)[/tex]

=> [tex]v_z = 0 \ m/s[/tex]

Generally the tangential velocity at that instant is mathematically represented as

[tex]v = -6.543 \^ i + 9.47 \^ j + 0 \^ k[/tex]

A Girl Swings A 0.250 Kg Rock Attached To A Taut String In A Circle Around Her Head. Her Hand Holds The

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