In a vertical lifting an object with mass of 2kg is lifted 1m above the ground. A work of 80J is done with a constant force. What is the acceleration of the object?
Fap = Force applied.
Fap*d = 80 J.
Fap*1 = 80, Fap = 80 N.
Fap = M*a. a = Fap/M. = 80/2 = 40 m/s^2.
To find the acceleration of the object, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done is given as 80 J.
First, let's calculate the gravitational potential energy gained by the object as it is lifted 1 meter above the ground. The formula for gravitational potential energy is:
Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
Given:
Mass (m) = 2 kg
Height (h) = 1 m
Acceleration due to gravity (g) = 9.8 m/s^2 (approximately)
Using the formula, we can calculate the potential energy gained:
PE = 2 kg * 9.8 m/s^2 * 1 m
= 19.6 J
As stated earlier, the work done is equal to the change in potential energy. Therefore:
Work (W) = Change in Potential Energy
W = PE - Initial Potential Energy
Since the object starts at ground level, the initial potential energy is zero. Substituting the values:
80 J = 19.6 J - 0
Now, rearranging the equation to isolate the change in potential energy:
Change in Potential Energy = 80 J
Since the object is lifted vertically, the change in potential energy is equal to the work done. Therefore:
80 J = 19.6 J
To find the acceleration, we can use the equation:
Work = Force * Distance
Rearranging the formula to isolate force:
Force = Work / Distance
Given:
Work (W) = 80 J
Distance = 1 m
Substituting the values into the formula:
Force = 80 J / 1 m
= 80 N
Now that we have the force, we can use Newton's second law of motion to find the acceleration:
Force = mass * acceleration
Substituting the values:
80 N = 2 kg * acceleration
Now, rearranging the equation to isolate acceleration:
acceleration = 80 N / 2 kg
= 40 m/s^2
Therefore, the acceleration of the object is 40 m/s^2.