A 60 kg worker pulls buckets of sand from height of 10 m using a pulley fixed to a wooden beam.While he is pulling a 20 kg bucket filled with sand he slips and falls down holding the rope.Assuming that the worker did not collide with bucket,find the velocity of the worker at the moment of striking the ground and the maximum height to which the bucket can ascend
net force down=g(60-20)=(total mass)a
a=40/80 g
vf^2=2a*10
the bucket: it is accelerating upward until it gets to 10 m, then has vf upward.
at the top...
vf^2=0= 20a+2g(h-10) solve for h.
To find the velocity of the worker at the moment of striking the ground, we can use the principle of conservation of energy. The potential energy of the worker when he is at a height of 10 m is converted into kinetic energy as he falls.
The potential energy (PE) at a certain height is given by the equation:
PE = mgh
where m is the mass, g is the acceleration due to gravity, and h is the height.
Given that the worker's mass is 60 kg and the height is 10 m, we can calculate the potential energy:
PE = (60 kg) * (9.8 m/s^2) * (10 m)
= 5880 joules
This potential energy is converted into kinetic energy, given by the equation:
KE = 1/2 * mv^2
where v is the velocity.
Therefore, we can equate the potential energy to the kinetic energy:
PE = KE
5880 joules = 1/2 * (60 kg) * v^2
Now we can solve for v:
v^2 = (2 * 5880 joules) / (60 kg)
v^2 = 196 m^2/s^2
Taking the square root of both sides:
v = √(196 m^2/s^2)
v ≈ 14 m/s
Therefore, the velocity of the worker at the moment of striking the ground is approximately 14 m/s.
To find the maximum height to which the bucket can ascend, we need to consider the conservation of mechanical energy for the sand bucket.
At the top of its motion, when the bucket is momentarily stationary, all the potential energy is converted into kinetic energy. At this point, the potential energy is maximum, and the kinetic energy is zero.
Using the same equation as before, substituting the values of mass and height for the bucket, we can calculate the potential energy:
PE = (20 kg) * (9.8 m/s^2) * (h_max)
Given the mass of the bucket is 20 kg, we can solve for h_max:
h_max = PE / (20 kg * 9.8 m/s^2)
h_max = 5880 joules / (20 kg * 9.8 m/s^2)
h_max ≈ 30 m
Therefore, the maximum height to which the bucket can ascend is approximately 30 m.