Determine the work done by a person when lowering an object of mass 2.6 kg by a distance of 2.4 m. The person applies a force Fext such that the object moves with constant speed, i.e., without acceleration,
W = F * d
and F = ma
but a = 0
so i was confused
To determine the work done by a person when lowering an object, we need to use the formula for work:
Work = Force x Distance x cos(θ)
In this case, the object is being lowered with constant speed, meaning there is no acceleration. According to Newton's second law, when there is no acceleration, the net force acting on the object is zero. Hence, the force applied by the person (Fext) must be equal to the weight of the object (mg), where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
So, Fext = mg
Given that the mass of the object is 2.6 kg, we can calculate the force applied by the person:
Fext = 2.6 kg × 9.8 m/s²
Now, we know the force and the distance (2.4 m) through which the object has been lowered. We can plug in these values into the work formula:
Work = Fext × Distance × cos(θ)
In this case, since the object is being lowered vertically, the angle (θ) between the force and the displacement is 0 degrees. Therefore, the cos(0°) will be equal to 1, and we can simplify the equation:
Work = Fext × Distance
Calculating the work:
Work = (2.6 kg × 9.8 m/s²) × 2.4 m
Solving this, we get the work done by the person to be the product of the force and distance, which is the final answer.