A 20 kg chair has 250 J of potential energy relative to the ground. If the chair is dropped from its position, what is its speed when it strikes the ground?
this is a response not to the problem but to bobpursley. how tf does this help at all, doesnt explain how to do the problem.
To find the speed of the chair when it strikes the ground, we can make use of the conservation of energy principle.
The potential energy of the chair is converted to kinetic energy as it falls.
The potential energy (PE) of an object near the surface of the Earth is given by the equation:
PE = m * g * h
Where:
PE is the potential energy
m is the mass of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height or distance from the ground or reference point
In this case, the mass (m) of the chair is 20 kg, and the potential energy (PE) is 250 J. We need to find the velocity or speed (v) of the chair when it hits the ground.
We can rearrange the equation for potential energy to solve for height (h):
h = PE / (m * g)
Substituting the given values:
h = 250 J / (20 kg * 9.8 m/s^2)
h = 1.275 m
Now, we can use the equation for the final velocity (v) of an object in free fall to solve for the speed of the chair when it strikes the ground:
v^2 = u^2 + 2 * g * h
Where:
v is the final velocity (what we want to find)
u is the initial velocity (which is zero because the chair is dropped)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height or distance the chair falls (1.275 m)
Plugging in the values:
v^2 = 0^2 + 2 * 9.8 m/s^2 * 1.275 m
v^2 = 2 * 9.8 m^2/s^2 * 1.275 m
v^2 = 24.99 m^2/s^2
To find v, we take the square root of both sides:
v = sqrt(24.99 m^2/s^2)
v = 5 m/s
Therefore, the speed of the chair when it strikes the ground is 5 m/s.
To find the speed at which the chair strikes the ground, we can use the principle of conservation of energy. The potential energy of an object is converted into kinetic energy as it falls.
The potential energy (PE) of the chair is given as 250 J, and its mass (m) is 20 kg. The formula for potential energy is:
PE = m * g * h
Where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height from which the chair is dropped.
To find the height, we can rearrange the formula and solve for h:
h = PE / (m * g)
= 250 J / (20 kg * 9.8 m/s^2)
≈ 1.28 meters
Now that we know the height, we can apply the principle of conservation of energy:
Potential Energy (PE) = Kinetic Energy (KE)
PE = KE
250 J = (1/2) * m * v^2
Rearranging this equation to solve for v (velocity):
v^2 = 2 * PE / m
v = √(2 * PE / m)
v = √(2 * 250 J / 20 kg)
v ≈ 7.97 m/s
Therefore, the speed at which the chair strikes the ground is approximately 7.97 m/s.
PE=final ke
mgh=1/2 mv^2 solve for v.