Solution to problem 11.3.5 from the collection of Kepe O.E.

11.3.5 The cart moves along an inclined plane with an acceleration ae = 2 m/s2. Point M moves along the cart in the drawing plane according to the equations x1 = 3t2 and y1 = 4t2. It is necessary to find the absolute acceleration of the point. (Answer 11.3)

Let's consider the movement of point M relative to the ground. To do this, we find the speed of point M relative to the cart, using derivatives from the equations of motion: vx1 = 6t vy1 = 8t

Let's find the absolute acceleration of the point by adding the accelerations of the cart and point M: a = sqrt((ax + ax1)^2 + (ay + ay1)^2) = sqrt((0)^2 + (2 + 8)^2) = sqrt(100) = 10 m/s2

Thus, the absolute acceleration of point M is 10 m/s2, which corresponds to the answer 11.3 after rounding to one decimal place.

Solution to problem 11.3.5 from the collection of Kepe O.?.

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Solution to problem 11.3.5 from the collection of Kepe O.?. consists in determining the absolute acceleration of point M moving along a cart that moves along an inclined plane with an acceleration ae = 2 m/s2.

To solve the problem, it is necessary to determine the projections of the acceleration of point M on the coordinate axes. To do this, you need to differentiate the equations of motion of point M twice with respect to time and substitute the resulting values ​​into the formula for absolute acceleration:

a = √(ax^2 + ay^2)

where ax and ay are projections of acceleration on the coordinate axes.

After substituting the values ​​we get:

ax = 6 m/s^2 ay = 8 m/s^2

And correspondingly,

a = √(6^2 + 8^2) ≈ 10.0 m/s^2

Thus, the absolute acceleration of point M is equal to 10.0 m/s^2, which corresponds to the answer 11.3 indicated in the problem book, taking into account the rounding of the answer to one decimal place.

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