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Alexandra [31]
3 years ago
7

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is find the speed of the block as it

reaches the bottom of the ramp, assuming it started sliding from rest at the top.
Physics
1 answer:
SashulF [63]3 years ago
6 0

Answer:

2.4\sqrt{L} where L is the length of the ramp

Explanation:

Let L (m) be the length of the ramp, and g = 9.81 m/s2 be the gravitational acceleration acting downward. This g vector can be split into 2 components: parallel and perpendicular to the ramp.

The parallel component would have a magnitude of

gsin\theta = 9.81 sin17^o = 2.87 m/s^2

We can use the following equation of motion to find out the final velocity of the book after sliding L m:

v^2 - v_0^2 = 2a\Delta s

where v m/s is the final velocity, v_0 = 0m/s is the initial velocity when it starts from rest, a = 2.87 m/s2 is the acceleration, and \Delta s = L is the distance traveled:

v^2 - 0 = 2*2.87*L

v = \sqrt{5.74L} = 2.4\sqrt{L}

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It would have been easier with the drawing. This problem is a projectile launching exercise, as they give us data after the window passes and the wall collides, let's calculate with this data the speeds at the point of contact with the window.

X axis

           x = Vox t

           t = x / vox

           t = 7.1 / 340

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             Vy = Voy - gt₂

             Vy = 0 -g t₂

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This is the time it also takes to travel the horizontal and vertical distance

            X = Vox t₂

            D = 340 2.83

            D = 962.2 m

           

            Y = Voy₂– ½ g t₂²

            Y = 0 - ½ g t2

            H = Y = - ½ 9.8 2.83 2

            H = 39.2 m

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