A drop hammer is lifted to a height of 50m above the ground and then allowed to fall from rest on to forging at ground level. Calculate the downward velocity of the hammer when it strikes the forging (g=10m/s)?
how long does it take to fall 50m? 4.9t^2 = 50
v = -9.8t
V^2 = Vo^2 + 2g*h = 0 + 20*60 = 1200,
V = __m/s.
To calculate the downward velocity of the hammer when it strikes the forging, we can use the principle of conservation of energy.
The potential energy (PE) of an object at a certain height is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the drop hammer is lifted to a height of 50m, so its potential energy at that height is PE = m * g * 50.
When the hammer falls and strikes the forging, all of its potential energy is converted into kinetic energy (KE). The formula for kinetic energy is KE = 0.5 * m * v^2, where v is the velocity of the hammer.
Therefore, we can equate the potential energy at the starting height to the kinetic energy just before striking the forging:
m * g * 50 = 0.5 * m * v^2.
We can cancel out the mass (m) from both sides of the equation:
g * 50 = 0.5 * v^2.
Rearranging the equation to solve for the velocity (v):
v^2 = 2 * g * 50,
v^2 = 1000,
v = √1000.
Calculating the square root of 1000, we get:
v ≈ 31.62 m/s.
Therefore, the downward velocity of the hammer when it strikes the forging is approximately 31.62 m/s.