For the Atwood's Machine
so the mass on the right side is 5 kg box which is 3m from the *table (represents the straight line)*
The left side of the pulley is 2kg box which is at the table.
1.) How do you know or what do you know about the force of tension in the rope acting on the two hanging masses?? Confused!!
2.) Quantitatively, the force of tension has to be_______ compared to the force of gravity on the 2 kg mass, and _______ compared to the force of gravity on the 5 kg.
How do you calculate the velocity of the 2 kg block when the 5 kg block hits the table?
1.) In the Atwood's Machine, the force of tension in the rope represents the force that is transmitted from one side of the pulley to the other side. Since the two masses are connected by a rope, the tension in the rope is the same for both masses. So, the force of tension in the rope is equal for both the 2 kg and 5 kg masses.
2.) Quantitatively, the force of tension in the rope is equal to the force of gravity on the smaller mass minus the force of gravity on the larger mass. In this case, the force of gravity on the 2 kg mass is given by the equation F = m * g, where m = mass (2 kg) and g = acceleration due to gravity (9.8 m/s^2). Therefore, the force of gravity on the 2 kg mass is 2 kg * 9.8 m/s^2 = 19.6 N.
On the other hand, the force of gravity on the 5 kg mass is 5 kg * 9.8 m/s^2 = 49 N. Therefore, the force of tension in the rope is 49 N - 19.6 N = 29.4 N.
Now, for the second part of the question about the velocity of the 2 kg block when the 5 kg block hits the table:
To calculate the velocity of the 2 kg block when the 5 kg block hits the table, you can use the principle of conservation of energy. At the start, when the system is released, it has a certain amount of gravitational potential energy. As the 5 kg block falls and hits the table, this potential energy is converted into kinetic energy. The kinetic energy gained by the 2 kg block can then be calculated.
The equation for calculating kinetic energy is given by the equation KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
To find the velocity of the 2 kg block, you need to first calculate the change in potential energy of the system. The initial potential energy is given by m * g * h, where m is the 5 kg mass, g is the acceleration due to gravity, and h is the vertical distance traveled by the 5 kg mass. In this case, h is 3 m.
The change in potential energy is then equal to the work done by the gravitational force, which is equal to the force of gravity multiplied by the distance traveled. Since the force of gravity is equal to the mass multiplied by the acceleration due to gravity, the change in potential energy can be written as (5 kg * 9.8 m/s^2) * 3 m.
This change in potential energy is equal to the kinetic energy gained by the 2 kg block, so you can equate the two expressions and solve for the velocity:
0.5 * (2 kg) * v^2 = (5 kg * 9.8 m/s^2) * 3 m
Now, you can solve this equation for v to find the velocity of the 2 kg block when the 5 kg block hits the table.