How much work does it take to raise a 3kg object 5m into the air?
(a) What is the potential energy of the object when it is 5m in the air? (b) What does this tell you about the potential energy you get when you do work to lift an object?
(c) If you drop the object, how fast is it going when it hits the ground? (d) What is the object’s kinetic energy when it hits the ground?
(e) Compare your answers to parts (b) and (d). What happens to the potential energy the object had?
To calculate the amount of work required to raise a 3kg object by 5m, you need to use the formula:
Work (W) = Force (F) x Distance (d) x cosθ
In this case, the force required to lift the object is its weight, which can be calculated using the formula:
Weight (W) = Mass (m) x Gravity (g)
The mass of the object is given as 3kg, and the acceleration due to gravity on Earth is approximately 9.8 m/s². Let's start by calculating the weight:
Weight = 3kg x 9.8m/s² = 29.4 N
Now, we can calculate the work:
Work = 29.4 N x 5m x cos(0°) = 147 J
(a) The potential energy of the object when it is 5m in the air is equal to the work done to raise it. So, the potential energy is 147 J.
(b) This tells us that the potential energy gained by lifting an object is equal to the work done on it. In this case, when the object is lifted, the work done is 147 J, which also represents the potential energy gained.
(c) If you drop the object, it will accelerate due to gravity. The final velocity when it hits the ground can be calculated using the formula:
Final velocity (v) = √(2 x g x h)
Where g is the acceleration due to gravity (9.8 m/s²) and h is the height (5m) from which the object was dropped. Let's calculate:
v = √(2 x 9.8m/s² x 5m) = √98 m/s ≈ 9.9 m/s
Therefore, the object will be traveling approximately 9.9 m/s when it hits the ground.
(d) The kinetic energy of the object when it hits the ground can be calculated using the formula:
Kinetic Energy (KE) = (1/2) x Mass (m) x Velocity (v)²
Substituting the values:
KE = (1/2) x 3kg x (9.9 m/s)² = 145.6 J
Thus, the object's kinetic energy when it hits the ground is approximately 145.6 J.
(e) Comparing the answers from part (b) and (d), we can see that the potential energy of the object when it was raised is equal to the kinetic energy of the object when it hits the ground. This is due to the conservation of energy principle, which states that energy cannot be created or destroyed, but only transferred or converted from one form to another. In this case, the potential energy of the raised object is converted into kinetic energy as it falls, resulting in the same total energy.