Question

1.) A material point moves in the x0y plane according to the law x = Asinωt, y = Bcosωt, where A,
B and ω are positive constants, A = B = 5 cm. Find the equation of the curve
describing the trajectory of the particle, depict its type and direction of motion of the
particle.

2.) The time dependence of the particle coordinate is given by the equation x = A + Bt + Ct2 +
Dt3
, where A = 0.1 m, B = 0.1 m / s, C = 0.14 m / s2
, D = 0.01 m / s3
. Find the average acceleration
and average speed over the first 10 seconds of movement.

3.) Two bars lie on a smooth table one on top of the other. The mass of the upper bar is m1 = 2 kg, of the
lower m2 = 4 kg. The coefficient of friction between the bars is k = 0.3. What is the
maximum force that can be applied to the upper bar in the horizontal
direction so that it does not slip?

4.) Two springs with a stiffness of 3⋅102
N / m and 6⋅102
N / m are connected in series.
Determine the work of stretching both springs if the second spring is stretched by
3 cm. Also determine the stiffness coefficient of the system of the two springs.

5.) The particle moves in a circle with a radius of 2 cm, while the dependence of its path on
time is given by the equation s = 0.1 t3
(cm). Find the tangential acceleration of the particle at
the moment when its linear velocity became 0.3 m / s.

Answer 1

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