at a construction site a crane lifts a block of mass,m,vertically upwards through a height of 70 m at constant speed by means of a strong cable.The block experiences a force of magnitude 8 N as a result of air friction as it is lifted vertically upwards.
The cable does 377 860 J of work in moving the block through a height of 70 m.calculate the mass of the block.
work done=mass*g*height+frictionforce*height
solve for mass.
should'nt i use the equetion mgh + half mv^2before=mgh + half mv^2aftr?
U=mgh
To calculate the mass of the block, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy.
In this case, the work done by the cable is equal to the change in potential energy of the block. Since the block is lifted vertically upwards, the work done by the cable is equal to the gravitational potential energy gained by the block.
The work done by the cable is given as 377,860 J, and the block is lifted through a height of 70 m. So, we can equate the work done to the change in potential energy:
Work done by the cable = Change in potential energy
377,860 J = m * g * h
Where:
m is the mass of the block,
g is the acceleration due to gravity (9.8 m/s^2),
h is the height the block is lifted (70 m).
Substituting the known values into the equation, we have:
377,860 J = m * 9.8 m/s^2 * 70 m
Simplifying the equation, we get:
377,860 J = 686 m
Now we can solve for the mass of the block:
m = 377,860 J / 686 kg/m
m ≈ 551 kg
Therefore, the mass of the block is approximately 551 kg.