A bucket of mass M = 5.47 kg is attached to a second bucket of mass m = 3:52 kg by an ideal string. The string is hung over an ideal pulley. Mass M is started with an intial downward speed of 2.13m/s. What then is the speed of mass (M) after it has moved 2.47m?
The answer should be 9.35m/s and I keep getting 9.40? What am I doing wrong
To find the final speed of mass M after it has moved a distance of 2.47m, we can use the concept of conservation of energy.
First, let's find the potential energy (PE) of mass M at the initial position:
PE1 = m1 * g * h1
where m1 is the mass of M, g is the acceleration due to gravity, and h1 is the initial height.
Since the bucket is moving downward initially, the initial height is 0, so PE1 = 0.
Next, let's find the potential energy (PE) of mass M after it has moved a distance of 2.47m. The height at this position is h2.
PE2 = m1 * g * h2
Now, let's find the kinetic energy (KE) of mass M at this position:
KE2 = (1/2) * m1 * v2^2
where v2 is the final velocity of M.
According to the principle of conservation of energy:
PE1 + KE1 = PE2 + KE2
Since PE1 = 0, the equation becomes:
KE1 = PE2 + KE2
Now, let's find the value of KE1:
KE1 = (1/2) * m1 * v1^2
where v1 is the initial velocity of M.
Substituting the given values:
KE1 = (1/2) * 5.47 kg * (2.13 m/s)^2
KE1 ≈ 12.13 J
Now, we can rearrange the equation and solve for v2:
KE2 = KE1 - PE2
(1/2) * m1 * v2^2 = KE1 - m1 * g * h2
v2^2 = (2 * (KE1 - m1 * g * h2)) / m1
v2 = sqrt((2 * (12.13 J - 5.47 kg * 9.8 m/s^2 * 2.47 m)) / 5.47 kg)
Calculating this equation will give you the final speed of mass M after it has moved 2.47m.