A kid with a mass of 30 kg slides down a slide 2.5 meters high from rest
a. What was his speed at the bottom?
b. If his speed was only 1 m/s at the bottom, how much energy was lost due to friction?
a. V^2 = Vo^2 + 2g*h
Vo = 0.
g = 9.8 m/s^2.
V = ?
b. PE-KE = M*g*h - 0.5M*V^2 = Energy lost.
V = 1 m/s.
To calculate the speed of the kid at the bottom of the slide, you can use the concept of conservation of energy. The potential energy at the top of the slide will be converted into kinetic energy at the bottom.
a. To determine the speed, we can equate the initial potential energy with the final kinetic energy:
Potential Energy at the top = Kinetic Energy at the bottom
Mgh = (1/2)mv^2
where:
m = mass of the kid (30 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the slide (2.5 m)
v = speed at the bottom
Substituting the given values:
(30 kg)(9.8 m/s^2)(2.5 m) = (1/2)(30 kg)v^2
735 J = 15v^2
Divide both sides by 15:
v^2 = 49 m^2/s^2
Taking the square root of both sides:
v = √49 m/s
v = 7 m/s
Therefore, the speed of the kid at the bottom of the slide is 7 m/s.
b. To calculate the energy lost due to friction, we need to find the difference between the initial and final total energy.
Initial total energy = Potential Energy at the top = mgh
Final total energy = Kinetic Energy at the bottom = (1/2)mv^2
Energy lost due to friction = Initial total energy - Final total energy
Energy lost due to friction = mgh - (1/2)mv^2
Substituting the given values:
Energy lost due to friction = (30 kg)(9.8 m/s^2)(2.5 m) - (1/2)(30 kg)(1 m/s)^2
Energy lost due to friction = 735 J - 15 J
Energy lost due to friction = 720 J
Therefore, if the speed at the bottom is only 1 m/s, 720 J of energy is lost due to friction.
To find the answers to these questions, we need to apply the principles of physics, specifically those related to energy and motion. Let's start with the first question:
a. What was his speed at the bottom?
To find the speed of the kid at the bottom of the slide, we can use the principle of conservation of energy. At the top of the slide, the kid only has potential energy equal to his mass (m) times the acceleration due to gravity (g) times the height of the slide (h), which is given by:
Potential Energy = m * g * h
At the bottom of the slide, all the potential energy has been converted into kinetic energy (KE) because there is no potential energy left. The kinetic energy is given by the formula:
Kinetic Energy = 0.5 * m * v^2
where v represents the speed of the kid at the bottom. Equating the potential energy to the kinetic energy, we get:
m * g * h = 0.5 * m * v^2
Simplifying the equation and solving for v, we find:
v = √(2 * g * h)
Substituting the given values, we have:
v = √(2 * 9.8 m/s^2 * 2.5 m)
Calculating this equation will yield the speed of the kid at the bottom of the slide.
Now, let's move on to the second question:
b. If his speed was only 1 m/s at the bottom, how much energy was lost due to friction?
To determine the energy lost due to friction, we need to find the initial kinetic energy at the top of the slide. Using the equation for kinetic energy mentioned earlier:
Initial Kinetic Energy = 0.5 * m * v_initial^2
where v_initial is the speed at the top of the slide. Since the kid starts from rest, v_initial will be zero.
Initial Kinetic Energy = 0.5 * m * (0 m/s)^2 = 0 Joules
The energy lost due to friction can be calculated by subtracting the final kinetic energy (at the bottom) from the initial kinetic energy:
Energy Lost = Initial Kinetic Energy - Final Kinetic Energy
Plugging in the given values:
Energy Lost = 0 Joules - (0.5 * m * v_final^2)
Energy Lost = - 0.5 * m * v_final^2
The negative sign indicates that energy is lost due to friction.