A 3.5 kg rock is initially at rest at the top of a cliff. Assuming the rock falls into the sea at the foot of the cliff and that its kinetic energy is transferred entirely to the water, how high is the cliff if the temperature of 0.88 kg of water is raised 0.10°C? (Neglect the heat capacity of the rock.)
To find the height of the cliff, we can use the principle of conservation of energy. The potential energy of the rock at the top of the cliff will be converted into the kinetic energy of the rock as it falls, which will then be transferred to the water in the form of thermal energy.
First, let's find the initial potential energy of the rock at the top of the cliff. The potential energy is given by the formula:
Potential Energy = mass * gravitational acceleration * height
Here, the mass of the rock is 3.5 kg, and the gravitational acceleration is approximately 9.8 m/s^2. Let's denote the height of the cliff as 'h'.
Potential Energy = 3.5 kg * 9.8 m/s^2 * h
The rock loses its potential energy as it falls, and this energy is transferred to the water. We can equate the potential energy to the change in thermal energy of the water. The change in thermal energy is given by the formula:
Change in Thermal Energy = mass of water * specific heat capacity of water * change in temperature
Here, the mass of the water is 0.88 kg, the specific heat capacity of water is approximately 4186 J/kg°C, and the change in temperature is 0.10°C.
Change in Thermal Energy = 0.88 kg * 4186 J/kg°C * 0.10°C
Since the kinetic energy transferred to the water is equal to the potential energy of the rock, we can equate the two equations:
3.5 kg * 9.8 m/s^2 * h = 0.88 kg * 4186 J/kg°C * 0.10°C
Now, we can solve for 'h' to find the height of the cliff.
heatgainedSea=original PE of frock
.88*cwater*deltaTemp=3.5*9.8*height
ok, solve for height.