A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 26.2 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 153 m), the block swings toward the outside of the curve. Then the string makes an angle θ with the vertical. Find θ.

Question

Rainbow

Physics

19 January, 04:32

A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 26.2 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 153 m), the block swings toward the outside of the curve. Then the string makes an angle θ with the vertical. Find θ.

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Answers (1)

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Armando Joseph · Answer 1

24.6 °

Explanation:

We have to:

Fn * sin (° A) = (m * v ^ 2) / r

Fn * cos (° A) = m * g

If we divide these two terms to obtain the tangent, we are left with:

Fn * sin (° A) 7Fn * cos (° A) = [ (m * v ^ 2) / r] / m * g

We solve and we are left with:

Tan (° A) = v ^ 2 / (g * r)

we know that the speed is 26.2 m / s, the gravity is 9.8 m / s ^ 2 and the radius is 153 m, we replace and we are left with:

Tan (° A) = 26.2 ^ 2 / (9.8 * 153)

Tan (° A) = 0.4578

(° A) = tan ^ - 1 (0.4578)

(° A) = 24.59 °

It means that the angle with the vertical is 24.6 °