A bobsled slides down an ice track starting
(at zero initial speed) from the top of a(n)
165 m high hill.
The acceleration of gravity is 9.8 m/s2 .
Neglect friction and air resistance and determine the bobsled’s speed at the bottom of
the hill.
Answer in units of m/s
PEofbobsled= finalKE
mgh=1/2 m v^2
solve for v. Notice mass divides out.
To determine the speed of the bobsled at the bottom of the hill, we can use the principles of conservation of energy. The initial potential energy of the bobsled at the top of the hill is converted into kinetic energy as it moves downhill.
The potential energy (PE) of an object is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
The equation for kinetic energy (KE) is given by KE = 0.5mv^2, where m is the mass of the object, and v is the velocity.
Since the bobsled starts from rest, its initial kinetic energy is zero. Therefore, the initial potential energy of the bobsled at the top of the hill is equal to the final kinetic energy of the bobsled at the bottom of the hill.
Setting the initial potential energy equal to the final kinetic energy:
mgh = 0.5mv^2
Simplifying the equation by canceling out the mass:
gh = 0.5v^2
Solving for v:
v^2 = 2gh
Substituting the given values:
v^2 = 2 * 9.8 m/s^2 * 165 m
v^2 = 3234 m^2/s^2
Taking the square root of both sides to solve for v:
v = √3234 m^2/s^2
v ≈ 56.9 m/s
Therefore, the bobsled's speed at the bottom of the hill is approximately 56.9 m/s.
To determine the speed of the bobsled at the bottom of the hill, we can use the principle of conservation of mechanical energy. The mechanical energy at the top of the hill (potential energy) will be converted into kinetic energy at the bottom of the hill.
The potential energy (PE) of the bobsled at the top of the hill can be calculated using the formula:
PE = mgh
Where m is the mass of the bobsled, g is the acceleration due to gravity, and h is the height of the hill. For this problem, the mass of the bobsled is not given, but since we are only interested in its speed, we can ignore it for now.
Given:
h = 165 m
g = 9.8 m/s^2
PE = mgh
Before substituting the values, we can solve for mgh:
mgh = (mass of bobsled) * (9.8 m/s^2) * (165 m)
= (mass of bobsled) * (1617 m^2/s^2)
From the equation, we can see that the units of mass are canceled out, so we don't need to know the mass of the bobsled.
Now, we can find the potential energy at the top of the hill.
PE = (1617 m^2/s^2)
The potential energy at the top of the hill is equal to the kinetic energy at the bottom of the hill:
KE = (0.5) * m * v^2
Where KE is the kinetic energy, v is the velocity (speed), and m is the mass of the bobsled (which we can ignore).
Setting the potential energy equal to the kinetic energy:
PE = KE
(1617 m^2/s^2) = (0.5) * m * v^2
Simplifying the equation:
v^2 = (2 * PE) / m
v^2 = (2 * 1617 m^2/s^2) / m
v^2 = (3234 m^2/s^2) / m
v^2 = 3234 m^2/s^2 * (1/m)
v^2 = 3234 m/s^2
Taking the square root of both sides to solve for v:
v = √(3234 m/s^2)
Now, we can calculate the speed of the bobsled at the bottom of the hill:
v ≈ 56.9 m/s
Therefore, the speed of the bobsled at the bottom of the hill is approximately 56.9 m/s.