You reach out a second-story window that is 17 m above the sidewalk and throw a 2-kg ball straing upward with 17 J of kinetic energy.
Use g = 10m/s^2
Part A) What is the ball's gravitational potential energy when it is released? Use a height measured from the sidewalk.
PE1 = m_ball*g*h_1 =_____________ Joules
Part B) What is the ball's gravitational potential energy just before hitting the sidewalk? Use a height measured from the sidewalk.
PE} = m_ball*g*h_2 =_____________ Joules
Part C) What is the ball's kinetic energy just before hitting the sidewalk? Since we have the conservation of energy we can assume that the energy from the beginning can convert to the final energy.
KE2 = PE1 + KE1 =
________________Joules
A ) m g h = 2 * 10 * 17 = 340 Joules
B ) zero
C ) at top Ke = 17 and Pe = 340
so at bottom where Pe = 0 then Ke = 357
I do not understand why you are asking because the problem leads you step by step to the solution.
To solve this problem, we can use the formulas for gravitational potential energy (PE) and kinetic energy (KE).
Given:
Height of the second-story window (h_1) = 17 m
Mass of the ball (m_ball) = 2 kg
Kinetic energy when released (KE1) = 17 J
Acceleration due to gravity (g) = 10 m/s^2
Part A) What is the ball's gravitational potential energy when it is released? Use a height measured from the sidewalk.
Gravitational potential energy formula:
PE1 = m_ball * g * h_1
Substituting the given values:
PE1 = 2 kg * 10 m/s^2 * 17 m
PE1 = 340 Joules
Therefore, the ball's gravitational potential energy when it is released is 340 Joules.
Part B) What is the ball's gravitational potential energy just before hitting the sidewalk? Use a height measured from the sidewalk.
Let's assume the height from the sidewalk just before hitting the sidewalk is h_2.
Gravitational potential energy formula:
PE2 = m_ball * g * h_2
Since the ball is at ground level when it hits the sidewalk, the height from the sidewalk (h_2) is 0.
Substituting the given values:
PE2 = 2 kg * 10 m/s^2 * 0 m
PE2 = 0 Joules
Therefore, the ball's gravitational potential energy just before hitting the sidewalk is 0 Joules.
Part C) What is the ball's kinetic energy just before hitting the sidewalk? Since we have the conservation of energy, we can assume that the energy from the beginning can convert to the final energy.
Conservation of energy states that the total energy at the beginning is equal to the total energy at the end.
Total energy at the beginning (TE1) = PE1 + KE1
TE1 = 340 Joules + 17 Joules
TE1 = 357 Joules
Since the ball falls freely, all its potential energy will convert to kinetic energy when it hits the ground.
Therefore, the ball's kinetic energy just before hitting the sidewalk would be equal to the total energy at the beginning because all the potential energy has converted to kinetic energy.
KE2 = TE1 = 357 Joules
Therefore, the ball's kinetic energy just before hitting the sidewalk is 357 Joules.
To solve these problems, we first need to understand the concepts of gravitational potential energy and kinetic energy.
Gravitational potential energy (PE) is the energy an object possesses because of its position relative to other objects due to gravity. The formula for gravitational potential energy is PE = m*g*h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
Kinetic energy (KE) is the energy possessed by an object due to its motion. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
Now let's solve the given problems:
Part A) What is the ball's gravitational potential energy when it is released? Use a height measured from the sidewalk.
Given:
Height (h) = 17 m
Mass (m) = 2 kg
Acceleration due to gravity (g) = 10 m/s^2
Using the formula for gravitational potential energy, we have:
PE1 = m * g * h1
Substituting the given values, we get:
PE1 = 2 kg * 10 m/s^2 * 17 m = 340 Joules
Therefore, the ball's gravitational potential energy when it is released is 340 Joules.
Part B) What is the ball's gravitational potential energy just before hitting the sidewalk? Use a height measured from the sidewalk.
In this case, the height (h2) is 0 because the ball is at the level of the sidewalk.
Using the formula for gravitational potential energy, we have:
PE2 = m * g * h2
Substituting the given values, we get:
PE2 = 2 kg * 10 m/s^2 * 0 m = 0 Joules
Therefore, the ball's gravitational potential energy just before hitting the sidewalk is 0 Joules.
Part C) What is the ball's kinetic energy just before hitting the sidewalk?
We know the ball's kinetic energy just after release is 17 Joules according to the problem statement. By the conservation of energy, this energy can be converted to kinetic energy just before hitting the sidewalk.
KE2 = PE1 + KE1
Substituting the given values, we get:
KE2 = 340 Joules + 17 Joules = 357 Joules
Therefore, the ball's kinetic energy just before hitting the sidewalk is 357 Joules.