A 30kg sled(with rider) slides without friction down a small, ice covered hill. On the first run the sled starts from rest and its speed at the bottom of the hill is 8.50m/s. On the second run the sled starts with a speed of 1.50m/s at the top. Find the speed of the sled at the bottom of the hill on the second run. Hint-find the total energy of the sled at the top of the hill for both cases.
Mg*h = 0.5M*V^2.
h = 0.5V^2/g = 0.5*8.5^2/9.8 = 3.69 m.
V^2 = Vo^2 + 2g*h.
Vo = 1.5 m/s.
g = 9.8 m/s^2.
V = ?
To find the speed of the sled at the bottom of the hill on the second run, we need to consider the conservation of energy. The total energy of the sled at the top of the hill is equal to the sum of its kinetic energy and potential energy.
Let's go through the steps to find the speed of the sled at the bottom of the hill on the second run:
1. Calculate the potential energy at the top of the hill for both cases.
- The potential energy (PE) is given by the equation PE = m * g * h, where m is the mass of the sled, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hill.
2. Calculate the kinetic energy at the top of the hill for both cases.
- The kinetic energy (KE) is given by the equation KE = 0.5 * m * v², where m is the mass of the sled and v is the velocity.
3. Calculate the total energy at the top of the hill for both cases.
- The total energy (TE) is the sum of the potential energy and kinetic energy.
4. Use the conservation of energy principle to find the speed at the bottom of the hill for the second run.
- The total energy at the top of the hill is equal to the total energy at the bottom of the hill, assuming no energy is lost due to friction.
- Set the total energy at the top of the hill for the second run equal to the total energy at the bottom of the hill for the first run, and solve for the velocity.
By following these steps, you can find the speed of the sled at the bottom of the hill on the second run.