# Danh mục: Mechanics

• ## The following parameters of the arrangement of Fig. 1.11 are available; the angle α which the inclined plane forms with the horizontal, and the coefficient of friction k between the body m1 and the inclined plane

The following parameters of the arrangement of Fig. 1.11 are available; the angle α which the inclined plane forms with the horizontal, and the coefficient of friction k between the body m1 and the inclined plane. The masses of the pulley and the threads, as well as the friction in the pulley, are negligible. Assuming […]

• ## A small body was launched up an inclined plane set at an angle α=15∘ against the horizontal. Find the coefficient of friction, if the time of the ascent of the body is η=2.0 times less than the time of its descent

A small body was launched up an inclined plane set at an angle ( alpha =15{}^circ )  against the horizontal. Find the coefficient of friction, if the time of the ascent of the body is  ( eta =2.0 ) times less than the time of its descent. Solution: Case 1. When the body is lauched […]

• ## Two touching bars 1 and 2 are placed on an inclined plane forming an angle α with the horizontal (Fig,. 1.10). The masses of the bars are equal to m1 and m2, and the coefficients of friction between the inclined plane and these bars are equal to k1 and k2 respectively, with k1>k2

Two touching bars 1 and 2 are placed on an inclined plane forming an angle α with the horizontal (Fig,. 1.10). The masses of the bars are equal to m1 and m2, and the coefficients of friction between the inclined plane and these bars are equal to k1 and k2 respectively, with ( {{k}_{1}}>{{k}_{2}} ). […]

• ## In the arrangement of Fig. 1.9 the masses m0, m1, and m2 of bodies are equal, the masses of the pulley and the threads are negligible, and there is no friction in the pulley. Find the acceleration w with which the body m0 comes down, and the tension of the thread binding together the bodies m1 and m2, if the coefficient of friction between these bodies and the horizontal surface is equal to Consider possible cases

In the arrangement of Fig. 1.9 the masses m0, m1, and m2 of bodies are equal, the masses of the pulley and the threads are negligible, and there is no friction in the pulley. Find the acceleration w with which the body m0 comes down, and the tension of the thread binding together the bodies […]

• ## An aerostat of mass m starts coming down with a constant acceleration w. Determine the ballest mass to be dumped for the aerostat to reach the upward acceleration of the same magnitude. The air drag is to be neglected.

An aerostat of mass m starts coming down with a constant acceleration Determine the ballest mass to be dumped for the aerostat to reach the upward acceleration of the same magnitude. The air drag is to be neglected. Solution: Let R be the constant upward thurst on the aerostat of mass m, coming down with […]

• ## Two particles, 1 and 2 moves with constant velocities v1 and v2. At the initial moment their radius vectors are equal to r1 and r2. How must these four vectors be interrelated for the particles to collide

Two particles, 1 and 2 moves with constant velocities v1 and v2. At the initial moment their radius vectors are equal to r1 and r2. How must these four vectors be interrelated for the particles to collide. Solution: Let the particles collide at the point A (Fig.) whose position vector is  ( {{vec{r}}_{3}} ) (say). […]

• ## A point moves rectilinearly in one direction. Fig. 1.1 shows the distance s traversed by the point as a function of the time Using the plot find

A point moves rectilinearly in one direction. Fig. 1.1 shows the distance s traversed by the point as a function of the time Using the plot find: (a) the average velocity of the point during the time of motion; (b) the maximum velocity; (c) the time moment t0 at which the instantaneous velocity is equal […]

• ## A car starts moving rectilinearly, first with acceleration w = 5.0 ms-2 (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate w, comes to a stop. The total time of motion equals τ = 25 s

A car starts moving rectilinearly, first with acceleration w = 5.0 ms-2 (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate w, comes to a stop. The total time of motion equals τ = 25 s. The average velocity during that time is equal to v = 72 […]

• ## A point traversed half the distance with a velocity v0. The remaining part of the distance was covered with velocity v1 for half the time, and with velocity v2 for the other half of the time

A point traversed half the distance with a velocity v0. The remaining part of the distance was covered with velocity v1 for half the time, and with velocity v2 for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion. Solution: Let s be the […]

• ## A motorboat going downstream overcame a raft at a point A; τ=60min later it turned back and after some time passed the raft at a distance ℓ=6.0kmfrom the point Find the flow velocity assuming the duty of the engine to be constant

A motorboat going downstream overcame a raft at a point A;  ( tau =60,,min )  later it turned back and after some time passed the raft at a distance  ( ell =6.0,,km )from the point Find the flow velocity assuming the duty of the engine to be constant. Solution: Let v0 be the stream velocity […]

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