You pick up a 2.5kg can of paint from the ground and lift it to a height of 1.7m .How much work do you do on the can of paint?
You hold the can stationary for half a minute, waiting for a friend on a ladder to take it. How much work do you do during this time?
m = 2.5 kg
h = 1.7 m.
Work=F*h = mg*h = 2.5*9.8*1.7=41.65 J.
No work is done when can is stationary.
To calculate the work done on the can of paint in the first scenario, you can use the formula:
Work = Force × Distance × cos(θ)
Given:
Mass of the can of paint (m) = 2.5 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Height (h) = 1.7 m
First, find the force required to lift the can by multiplying the mass and the acceleration due to gravity:
Force = mass × acceleration due to gravity
= 2.5 kg × 9.8 m/s^2
= 24.5 N
Next, calculate the work done on the can by multiplying the force, distance, and the cosine of the angle between the force and the direction of motion (which is 0 degrees here, since the force and the displacement are in the same direction):
Work = Force × Distance × cos(θ)
= 24.5 N × 1.7 m × cos(0 degrees)
= 24.5 N × 1.7 m × 1
= 41.65 Joules
Therefore, the work done on the can of paint while lifting it to a height of 1.7 meters is 41.65 Joules.
In the second scenario, you are holding the can stationary, which means there is no displacement. Hence, no work is being done during this time.
To calculate the work done, you need to use the formula:
Work = Force x Distance x cos(theta)
Where:
- Force is the applied force in the direction of motion,
- Distance is the displacement of the object,
- theta is the angle between the applied force and the direction of motion.
In the first scenario, you lift the can of paint vertically upwards to a height of 1.7m. The force required to lift an object vertically is equal to its weight.
Weight = mass x gravity
Given that the mass of the can is 2.5kg and the acceleration due to gravity is approximately 9.8 m/s², you can calculate the weight:
Weight = 2.5kg x 9.8 m/s² = 24.5 N
The distance lifted is 1.7m. Since the force and the displacement are in the same direction, the angle theta between them is 0°.
Now you can calculate the work done:
Work = 24.5 N x 1.7m x cos(0°) = 24.5 N x 1.7m x 1 = 41.65 Joules
Therefore, you do 41.65 Joules of work on the can of paint when lifting it to a height of 1.7m.
In the second scenario, where you hold the can stationary for half a minute, no work is done on the can. Work is defined as the transfer of energy resulting from an applied force over a distance, and since there is no displacement, the work done is zero.
So, during the half-minute waiting period, you do zero work on the can.