Final answer:
To determine the speed of a block at the bottom of a 5 meter ramp, we use conservation of energy and the equation v = √(2gh), assuming no friction. The mass of the block cancels out and is not needed to calculate the final speed.
Step-by-step explanation:
Calculating Speed at the Bottom of a Ramp
A block is released from rest at the top of a ramp and we are asked to determine its speed at the bottom, given that the ramp is 5 meters long and friction is to be neglected.
To find the speed of the block at the bottom, we can use the principle of conservation of energy, which states that the total mechanical energy of the block remains constant if no external work is done on the system (friction is neglected in this case).
Initially, the block has potential energy due to its height above the ground level. As it slides down the ramp, this potential energy is converted into kinetic energy.
Assuming the height of the ramp (h) is known and using gravitational acceleration (g = 9.81 m/s2), the initial potential energy (mgh) will be equal to the kinetic energy (½mv2) at the bottom of the ramp. Here, 'm' stands for the mass of the block and 'v' is the velocity we want to find.
Since mass appears on both sides of the equation, it cancels out, allowing us to solve for 'v' without needing to know the mass of the block.
The formula used to determine the final speed ('v') at the bottom is given by:
v = √(2gh)
This enables us to calculate the speed at the bottom of the ramp using just the height of the ramp and the acceleration due to gravity.