CONSERVATION OF ENERGY
A 2kg object is tossed upward with a kinetic energy of 220 J. How high does the object travel?
To solve this problem, we can use the conservation of energy principle, which states that the total energy of a system remains constant.
Initially, the object has a kinetic energy of 220 J. As it moves upward, the kinetic energy is converted into potential energy. At its highest point, when it momentarily stops, all of its kinetic energy is converted into potential energy.
The potential energy (PE) of an object at a height (h) is given by the equation:
PE = mgh
Where m is the mass of the object (2 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
To calculate the height (h), we can rearrange the equation to solve for h:
h = PE / (mg)
Plugging in the values, we get:
h = 220 J / (2 kg * 9.8 m/s^2)
h = 22.45 m
Therefore, the object travels approximately 22.45 meters high.
To determine how high the object travels, we can use the principle of conservation of energy. The initial kinetic energy of the object is converted into potential energy as it moves upward against the force of gravity.
The potential energy (PE) of an object in a gravitational field is given by the equation:
PE = mgh
Where:
m = mass of the object (2 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height
Since the object starts with an initial kinetic energy (KE) of 220 J, we can equate the initial kinetic energy to the potential energy:
KE = PE
220 J = mgh
Now, let's solve for h, the height at which the object travels:
h = (220 J) / (mg)
Substituting the values, we have:
h = (220 J) / (2 kg * 9.8 m/s^2)
h = 11.22 meters
Therefore, the object reaches a height of 11.22 meters.
To determine how high the object travels, we can use the principle of conservation of energy. The total mechanical energy of the object is conserved throughout its motion, meaning that the initial kinetic energy will be equal to the gravitational potential energy at the highest point of its trajectory.
Given:
Mass of the object (m) = 2 kg
Initial kinetic energy (KE_initial) = 220 J
The kinetic energy of an object can be calculated using the formula:
KE = (1/2) * m * v^2
Where v represents the velocity of the object.
Rearranging the formula, we can solve for v:
v = sqrt((2 * KE) / m)
Now, we can calculate the velocity (v) of the object using the given kinetic energy and mass:
v = sqrt((2 * 220 J) / 2 kg)
v = sqrt(440 J / 2 kg)
v = sqrt(220 m^2/s^2 / 2 kg)
v = sqrt(110 m^2/s^2/kg)
As we want to find the height, we need to determine the final gravitational potential energy (PE_final) of the object. This can be calculated using the formula:
PE = m * g * h
Where g represents the acceleration due to gravity and h represents the height.
Rearranging the formula, we can solve for h:
h = PE / (m * g)
The gravitational potential energy (PE) can be calculated using the formula:
PE = m * g * h
Now, we can calculate the height (h) of the object:
h = PE / (m * g)
h = KE_initial / (m * g)
h = 220 J / (2 kg * 9.8 m/s^2)
h = 220 J / (19.6 kg * m/s^2)
h = 220 J / 19.6 kg*m/s^2
h = 11.22 m
Therefore, the object travels to a height of approximately 11.22 meters.