A mass m1 = 4.9 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 4.7 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.8 m.
To solve this problem, we can use the concept of conservation of energy. Since the table is frictionless, the only forces acting on the system are gravity and tension in the string.
First, let's calculate the potential energy (PE) of the hanging mass when it has fallen a distance d. The expression for potential energy is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
PE2 = m2 * g * d
= 4.7 kg * 9.8 m/s^2 * 0.8 m
= 36.8624 J
Next, let's consider the potential energy of the other mass when it moves upward a distance d. Since the two masses are connected by a string passing over a pulley, when one mass moves up, the other moves down by the same distance. So, the potential energy gained by the first mass equals the potential energy lost by the second mass.
PE1 = PE2
Now, let's calculate the potential energy of the first mass. The potential energy is given by PE = mgh.
PE1 = m1 * g * d
Substituting the known values:
36.8624 J = 4.9 kg * 9.8 m/s^2 * d
Now we can solve for the distance d:
d = 36.8624 J / (4.9 kg * 9.8 m/s^2)
≈ 0.757 m
So, the distance the mass on the table moves upward is approximately 0.757 meters.