Calculate the kinetic energy acquired by a 11- nail when it is struck by a 540- hammer moving with an initial speed of 4.9 .
KE= 1/2 m v^2
normally, in the SI system, for KE to be in joules, mass has to be in kilograms, and velocity in meters per second.
To calculate the kinetic energy acquired by the nail when it is struck by the hammer, we can use the formula for kinetic energy:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
First, let's calculate the mass of the hammer by converting its weight to mass:
Weight = mass * acceleration due to gravity
Given that the weight of the hammer is 540 N, and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation to solve for mass:
mass = Weight / acceleration due to gravity
mass = 540 N / 9.8 m/s^2
mass ≈ 55.1 kg
Now we have the mass of the hammer. Next, we need to determine the velocity of the hammer just before it strikes the nail. The problem states that the hammer is moving with an initial speed of 4.9 m/s.
Since we are assuming that no external forces are acting on the hammer-nail system after the collision, the principle of conservation of momentum can be applied. Therefore, the velocity of the hammer just after the collision will be the same as the initial speed (4.9 m/s).
Now we can substitute the values into the formula for kinetic energy:
KE = 0.5 * mass * velocity^2
KE = 0.5 * (mass of the nail) * (velocity of the nail)^2
Since no information is provided about the nail's mass or velocity, we can't calculate the exact value of kinetic energy. However, the equation is set up correctly for calculation once the nail's mass and velocity are known.