A 0.400 kg block of wood hangs from the ceiling by a string, and a 0.0700 kg wad of putty is thrown straight upward, striking the bottom of the block with a speed of 6.40 m/s. The wad of putty sticks to the block.
How high does the putty-block system rise above the original position of the block?
I'm confused as to what equation to use. None of them seem to fit the bill perfectly.
I have solved this problem.
use conservation of momentum to get the velocity of the block/putty after collision. Then, using that initial vertical velocity, compute the altitude
vi^2=2g*height
To solve this problem, we can apply the principle of conservation of mechanical energy. The initial potential energy of the block is converted into the final potential energy of the block-putty system.
Here are the steps to find the height the putty-block system rises above the original position of the block:
Step 1: Calculate the initial potential energy of the block.
The initial potential energy (PE) of the block is given by the formula:
PE_initial = m_block * g * h_initial
where m_block is the mass of the block and h_initial is the initial height of the block.
Step 2: Calculate the final potential energy of the block-putty system.
The final potential energy (PE_final) of the block-putty system is given by the formula:
PE_final = (m_block + m_putty) * g * h_final
where m_block is the mass of the block, m_putty is the mass of the putty, g is the acceleration due to gravity, and h_final is the final height of the block-putty system.
Step 3: Apply the conservation of mechanical energy.
According to the conservation of mechanical energy, the initial potential energy of the block is equal to the final potential energy of the block-putty system:
PE_initial = PE_final
Step 4: Substitute the known values.
For the given problem, the mass of the block (m_block) is 0.400 kg, the mass of the putty (m_putty) is 0.0700 kg, the acceleration due to gravity (g) is 9.81 m/s^2, and the initial height (h_initial) is zero.
Step 5: Solve for the final height (h_final).
Rearrange the equation from Step 3 to solve for h_final:
h_final = PE_initial / [(m_block + m_putty) * g]
Step 6: Calculate the final height.
Substitute the known values into the formula from Step 5 and calculate the height.
Once you plug in the numbers and perform the calculations, you should be able to find the height the putty-block system rises above the original position of the block.