Two blocks with masses m1 = 3.9 kg and m2 = 6.7 kg are connected by a string that hangs over a pulley of mass M = 2.2 kg and radius R = 0.11 m as shown above. The string does not slip. Assuming the system starts from rest, use energy principle find the speed of m2 after it has fallen by 0.4 m. Treat the pulley as a disk.
This is your sixth post that I have looked at. In NONE do I see any evidence of YOUR work. Are you merely flooding the board with your questions? If so, you will get no answer. We HELP here by answering questions you post, but we do not DO the work for you.
Sra
the work is on a forum that actually helps ppl
To find the speed of m2 after it has fallen by 0.4 m, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of a system remains constant if no external work is done on the system.
In this case, the only external force acting on the system is gravity. Let's break down the steps to find the speed of m2:
1. Calculate the potential energy of m2 at the initial position:
The potential energy of an object of mass m located at a height h is given by: P.E. = m * g * h, where g is the acceleration due to gravity (9.8 m/s²). In this case, m2 falls by 0.4 m, so the initial potential energy of m2 is given by: P.E.(initial) = m2 * g * 0.4.
2. Calculate the work done against gravity as m2 falls:
The work done against gravity on m2 is given by: Work = force * distance. Since gravity acts downward, the force exerted by gravity is given by the weight of m2, which is equal to m2 * g. The distance is the height through which m2 falls, which is 0.4 m. Therefore, Work = (m2 * g) * 0.4.
3. Calculate the potential energy of m1 at the initial position:
Similarly, m1 is lifted by 0.4 m, so the initial potential energy of m1 is given by: P.E.(initial) = m1 * g * 0.4.
4. Calculate the rotational kinetic energy of the pulley at the initial position:
The rotational kinetic energy of a disk is given by the equation: K.E.(rotational) = (1/2) * I * ω², where I is the moment of inertia and ω is the angular velocity. For a disk, the moment of inertia is given by: I = (1/2) * M * R², where M is the mass of the pulley and R is its radius. Since the pulley is at rest initially, its angular velocity is zero, so its rotational kinetic energy is also zero.
5. Calculate the total initial mechanical energy:
The total initial mechanical energy is the sum of the initial potential energies of m1 and m2, and the initial rotational kinetic energy of the pulley.
6. Calculate the potential energy of m2 at the final position:
Since m2 has fallen by 0.4 m, its potential energy at the final position is given by: P.E.(final) = m2 * g * 0.
7. Calculate the final kinetic energy of m2:
The final kinetic energy of m2 is given by: K.E.(final) = (1/2) * m2 * v², where v is the speed of m2 at the final position.
8. Apply the principle of conservation of mechanical energy:
According to this principle, the total initial mechanical energy is equal to the total final mechanical energy, neglecting any losses. Therefore, we can equate the total initial mechanical energy to the sum of the final potential energy of m2 and the final kinetic energy of m2.
9. Solve for the speed of m2:
Rearrange the equation obtained in step 8 to solve for v, the speed of m2 at the final position.
By following these steps, you can calculate the speed of m2 after it has fallen by 0.4 m using the energy principle.