A person lifts a 5.5 kg cement block a vertical distance 1.1 m and then carries the block horizontally a distance 7.3 m. Determine the work done by the person and by the force of gravity in this process.
J (by person)
J (by force of gravity)
No work is done during the horizontal motion.
The vertical-motion work done by the person is m g h. (h = 1.1 m)
Gravity does the same amount, but qwith a minus sign.
To determine the work done by the person and by the force of gravity, we first need to understand the concept of work.
Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) is given by the equation:
W = F * d * cosθ
Where:
- W is the work done
- F is the force applied
- d is the displacement of the object
- θ is the angle between the force and displacement vectors
In this scenario, the person lifts the cement block vertically and then carries it horizontally. Let's analyze both parts separately to determine the work done.
1. Vertical Lift:
The person lifts the cement block vertically against the force of gravity. We assume there is no acceleration, so the force applied by the person must be equal in magnitude to the force of gravity acting on the block.
In this case, the displacement (d) is given as 1.1 m, and the angle (θ) between the force and displacement vectors is 0 degrees since the force and displacement are in the same direction. Therefore, cosθ = 1.
To find the force (F) applied by the person, we use Newton's second law:
F = m * g
Where:
- m is the mass of the block (5.5 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
Now we can calculate the work (W) done by the person:
W = F * d * cosθ = (m * g) * d * cosθ
2. Horizontal Carry:
In this part, the person carries the block horizontally. Since the force of gravity acts vertically downwards, it is perpendicular to the displacement vector. Therefore, the angle (θ) between the force and displacement vectors is 90 degrees, and cosθ = 0.
However, the force of gravity is still acting on the block, causing negative work. The displacement (d) is given as 7.3 m.
To calculate the work (W) done by the force of gravity:
W = F * d * cosθ = (m * g) * d * cosθ
Now, plug in the values in both formulas to obtain the work done by the person and by the force of gravity.