A 55.0 kg child slides down from rest from the top of a water slide that is 5.0 m long and inclined 300 with the horizontal. The child reaches the bottom of the slide with a speed of 6.24 m/s. Find his total mechanical energy at the top of the slide.
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To find the total mechanical energy at the top of the slide, we need to calculate the potential energy (PE) and the kinetic energy (KE) of the child.
1. Calculate the potential energy (PE) at the top of the slide using the formula:
PE = m * g * h
where m is the mass of the child (55.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height difference between the top and bottom of the slide.
2. Calculate the height (h) using trigonometry:
h = L * sin(θ)
where L is the length of the slide (5.0 m) and θ is the angle of inclination (30 degrees).
3. Plug in the values into the equation to find the potential energy (PE):
PE = 55.0 kg * 9.8 m/s^2 * (5.0 m * sin(30 degrees))
4. Next, calculate the kinetic energy (KE) at the bottom of the slide using the formula:
KE = (1/2) * m * v^2
where v is the velocity of the child at the bottom of the slide (6.24 m/s).
5. Plug in the values into the equation to find the kinetic energy (KE):
KE = (1/2) * 55.0 kg * (6.24 m/s)^2
6. Finally, add the potential energy (PE) and kinetic energy (KE) to find the total mechanical energy:
Total mechanical energy = PE + KE
Note: Make sure to convert angles to radians if necessary and perform the calculations accurately to get the correct final answer.
To find the total mechanical energy at the top of the slide, we need to consider the potential energy and kinetic energy of the child.
First, let's find the potential energy (PE) of the child at the top of the slide. The formula for potential energy is:
PE = m * g * h
Where:
m = mass of the child (55.0 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the slide (5.0 m)
Let's calculate the potential energy:
PE = 55.0 kg * 9.8 m/s^2 * 5.0 m
Next, let's find the kinetic energy (KE) of the child at the top of the slide. The formula for kinetic energy is:
KE = (1/2) * m * v^2
Where:
m = mass of the child (55.0 kg)
v = speed of the child (0 m/s - since the child is at rest at the top of the slide)
Let's calculate the kinetic energy:
KE = (1/2) * 55.0 kg * 0 m/s^2
Now, the total mechanical energy (E) is the sum of potential energy and kinetic energy:
E = PE + KE
Since the child is at rest at the top of the slide, the kinetic energy is zero. Therefore, the total mechanical energy at the top of the slide is equal to the potential energy:
E = PE = 55.0 kg * 9.8 m/s^2 * 5.0 m
Now, you can calculate the total mechanical energy at the top of the slide using the given values.