At a playground, a 22kg child plays on a slide that drops through a height of 2.1m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -371J on the child.
What is the child's speed at the bottom of the slide?
idk lol
To determine the child's speed at the bottom of the slide, we need to apply the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
Work = Change in Kinetic Energy
In this case, the work done by the slide on the child is given as -371J (negative because the work is done by a non-conservative force).
The change in kinetic energy of the child can be calculated using the formula:
Change in Kinetic Energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
Since the child starts at rest, their initial velocity is 0 m/s.
Therefore, we can write the equation as:
-371J = (1/2) * 22kg * (final velocity^2 - 0^2)
Simplifying the equation:
-371J = 11kg * final velocity^2
Dividing both sides by 11kg:
-371J / 11kg = final velocity^2
Rearranging the equation:
final velocity^2 = -371J / 11kg
Taking the square root of both sides to solve for the final velocity:
final velocity = sqrt(-371J / 11kg)
Note: The negative sign in front of the work done (-371J) indicates that the force is acting opposite to the motion, resulting in negative work. However, the speed is always a positive value, so we will consider the magnitude of the velocity.
Now, we can calculate the value:
final velocity = sqrt(-371J / 11kg)
Using a calculator:
final velocity ≈ 6.03 m/s
Therefore, the child's speed at the bottom of the slide is approximately 6.03 m/s.
To find the child's speed at the bottom of the slide, we need to apply the principle of conservation of energy. The total mechanical energy of the child at the top of the slide is equal to the total mechanical energy at the bottom of the slide, considering no other external forces.
The total mechanical energy (TE) can be expressed as the sum of the kinetic energy (KE) and the gravitational potential energy (PE):
TE = KE + PE
The kinetic energy (KE) is given by the formula KE = (1/2) * m * v^2, where 'm' is the mass of the child and 'v' is the speed of the child.
The gravitational potential energy (PE) is given by the formula PE = m * g * h, where 'm' is the mass of the child, 'g' is the acceleration due to gravity (approximately 9.8 m/s^2), and 'h' is the height of the slide.
Since the slide does negative work on the child, it means that some of the potential energy is converted into nonconservative work. This negative work can be subtracted from the total mechanical energy to determine the final kinetic energy:
TE - Work = KE
In this case, the work done by the slide is given as -371J. Hence:
TE - (-371J) = KE
Now we can substitute the formulas for KE and TE, and solve for 'v':
(1/2) * m * v^2 - (-371J) = m * g * h
Plugging in the given values:
(1/2) * 22kg * v^2 - (-371J) = 22kg * 9.8 m/s^2 * 2.1m
Simplifying and solving for 'v':
11kg * v^2 + 371J = 441.42kg.m^2/s^2
11kg * v^2 = 441.42kg.m^2/s^2 - 371J
11kg * v^2 = 441.42kg.m^2/s^2 + (-371J)
11kg * v^2 = 441.42kg.m^2/s^2 + (-371kg.m^2/s^2)
11kg * v^2 = 70.42kg.m^2/s^2
v^2 = 70.42kg.m^2/s^2 / 11kg
v^2 ≈ 6.402m^2/s^2
v ≈ √(6.402m^2/s^2)
v ≈ 2.53m/s
Therefore, the child's speed at the bottom of the slide is approximately 2.53 m/s.
V^2 = Vo^2 + 2g*h.
Vo = 0.
g = 9.8 m/s^2.
h = 2.1 m.
V = ?