Hi im kinda confused still on Pulley systems and hoping someone can help me out.
The two masses (m1 = 5.5kg and m2 = 3.0kg) in the Atwood's machine shown in The Figureare released from rest, with at a height of 0.89m above the floor. When m1 hits the ground its speed is 1.8 m/s.
Assuming that the pulley is a uniform disk with a radius of 12 , outline a strategy that allows you to find the mass of the pulley.
Does this have to with conservation of energy in someway? Kinda confused.
yes. The energy in the mass falling, and the energy in the mass going up, and the KE of the pulley, are equal to the total initial GPE.
That makes sense, but what kinda of formula would i then use to solve it? I;m only going off of powerpoints its kinda bad.
Intial PEmass1+ initialPEmass2 =finalKEmass2+FinalKEmass1+finalKEpulley+finalPEmass2+finalPEmass1
yarý çapý 1 cm olan kürenin yarýçapý 2 katýna çýkarýldýgýnda kesit alaný ,yüzey
Yes, you are correct! The strategy to find the mass of the pulley involves the principle of conservation of energy. The basic idea is to equate the potential energy lost by the masses to the rotational kinetic energy gained by the pulley.
Here's a step-by-step strategy to find the mass of the pulley:
Step 1: Calculate the potential energy of the masses before they are released. The potential energy formula is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
For mass m1:
PE1 = m1 * g * h
Step 2: Calculate the total kinetic energy of the system after mass m1 hits the ground. The kinetic energy formula is KE = (1/2)mv^2, where m is the mass and v is the velocity.
For mass m1:
KE1 = (1/2) * m1 * v1^2, where v1 is the velocity of mass m1 when it hits the ground (given as 1.8 m/s)
Step 3: Calculate the difference in potential energy and kinetic energy, which represents the energy absorbed by the pulley. This energy is converted into the rotational kinetic energy of the pulley.
ΔE = PE1 - KE1
Step 4: Calculate the moment of inertia (I) of the pulley. The moment of inertia of a uniform disk is given by I = (1/2) * m * r^2, where m is the mass of the pulley and r is the radius.
Step 5: Calculate the rotational kinetic energy (KE_rot) of the pulley using the moment of inertia and the equation KE_rot = (1/2) * I * ω^2, where ω is the angular velocity.
Step 6: Equate the energy absorbed by the pulley (ΔE) to the rotational kinetic energy of the pulley (KE_rot) and solve for the mass of the pulley (m).
ΔE = KE_rot
(m1 * g * h) - ((1/2) * m1 * v1^2) = (1/2) * (1/2) * m * r^2 * ω^2
Step 7: Solve the equation for m, the mass of the pulley.
m = [(2 * (m1 * g * h - (1/2) * m1 * v1^2)) / (r^2 * ω^2)]
Remember to ensure proper unit conversions and use the correct value for the acceleration due to gravity (g) in the calculations.
I hope this step-by-step strategy helps you solve the problem and find the mass of the pulley!