The two blocks in an Atwood machine have masses 2 ·0 kg and 3 ·0 kg . Find the work done by gr

The two blocks in an Atwood machine have masses 2 ·0 kg and...

The two blocks in an Atwood machine have masses $2 \cdot 0 \mathrm{~kg}$ and $3 \cdot 0 \mathrm{~kg} .$ Find the work done by gravity during the fourth second after the system is released from rest.

Key Concepts

Atwood Machine Dynamics

The Atwood machine is a classic physics apparatus used to study the motion of connected masses. Its analysis involves applying Newton's second law to a system where two masses are linked by a string over a pulley, resulting in a net acceleration determined by the difference in gravitational forces acting on the masses relative to their total mass.

Work Done by a Force

Work is defined as the product of the force component in the direction of displacement and the magnitude of that displacement. When calculating the work done by a force like gravity, one must integrate or multiply the gravitational force by the vertical displacement over which it is applied, taking into account the sign related to the direction of motion.

Uniformly Accelerated Motion

Many mechanics problems involve objects moving under constant acceleration. Kinematic equations that connect displacement, time, velocity, and acceleration are crucial for determining distances traveled during specific time intervals. Such equations are particularly important when analyzing the segment of motion, like a specific second, within the overall motion of the system.

Gravitational Force

Gravity imparts a constant acceleration to objects near the Earth's surface, and its force on an object is given by the product of its mass and the acceleration due to gravity. In dynamics problems, the gravitational force is a key component for understanding both the net force in systems like the Atwood machine and the work done by gravity as an object moves vertically.

Transcript

00:01 Okay in this question two blocks in an atwood machine have mass is 2 kg and 3 kg okay so this is the atwood machine okay and this is the pulley and here the mass and this is the mass okay so here the mass is 3 kg and the smaller one is 2 kg okay so here we can say the tension will free body diagram of this 3k g mass it will be like this this is a 3kg okay tension will be like this and the gravitational force like m g that is it will be 3g okay and it will goes to the downside it will goes to the upside so the resultant okay resultant it will be here and it will be m so it will be 3a okay and now we will do the free body diagram of this 2 kg mass okay so this 2 kg okay and the tension upward and m g that is 2g okay it will be downward and it is goes upward so resultant it will be upside okay and that is m a so it will be 2a okay so here we can find out the relation okay so resultant here 3a okay that is downward so it will be 3g minus t understand so from here t will be 3g minus 3a okay and now from here t will be 3g minus 3a okay and now from this 2 kg mass, the resultant that is upward that is 2a, it will be t minus 2g.

01:36 And now we will put the value of t from here into the second equation.

01:40 So 2a that is equal to t that is 3g minus 3a minus 2g.

01:45 So this 3a will go on the left hand side.

01:47 So it will be 5a equals to 3g minus 2g that is g.

01:51 So a will be g divided by 5.

01:54 So this is the acceleration we have got.

01:56 And now what is to be done in the question? we have to find out the work done by the gravity during the 4th second after the system is released from the rest...

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