You pick up a 3.2 kg can of paint from the ground and lift it to a height of 1.4 m .
Part A
How much work do you do on the can of paint?
Express your answer to two significant figures and include the appropriate units.
Part B
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?
Express your answer to two
significant figures and include the appropriate units.
Part C
Your friend decides not to use the paint, so you lower it back to the ground. How much work do you do on the can as you lower it?
Express your answer to two significant figures and include the appropriate units.
Part A:
To calculate the work done on the can of paint when lifting it to a height of 1.4 m, we can use the formula:
Work = Force × Distance × cos(θ)
In this case, the force is equal to the weight of the can, which can be calculated using the equation:
Weight = mass × gravitational acceleration
Weight = 3.2 kg × 9.8 m/s^2
Next, we need to find the distance moved, which is 1.4 m. Lastly, the angle (θ) between the force and the direction of motion is 0 degrees since the force and motion are in the same direction.
Now, we can calculate the work done:
Work = (Weight) × (Distance) × cos(θ)
Work = (3.2 kg × 9.8 m/s^2) × 1.4 m × cos(0°)
Work ≈ 43 J
Therefore, the work done on the can of paint is approximately 43 Joules.
Part B:
When holding the can stationary, no work is done because there is no displacement of the can. The formula to calculate work is:
Work = Force × Distance × cos(θ)
In this case, the distance moved is zero since the can is held stationary. Therefore, the work done is zero.
Work = 0 J
Part C:
To calculate the work done on the can as you lower it back to the ground, we apply the same formula:
Work = Force × Distance × cos(θ)
The force is still the weight of the can, which is the same as in Part A. The distance moved is 1.4 m, and the angle (θ) between the force and the direction of motion is 180 degrees since the force and motion are in opposite directions.
Work = (Weight) × (Distance) × cos(θ)
Work = (3.2 kg × 9.8 m/s^2) × 1.4 m × cos(180°)
Work ≈ -43 J
The negative sign indicates that work is being done against the force of gravity.
Therefore, the work done on the can as you lower it back to the ground is approximately -43 Joules.
To calculate the work done, we can use the formula:
Work (W) = force (F) x distance (d) x cos(theta)
where:
- Force is the gravitational force acting on the can, which is given by the weight of the can. The weight (W) is calculated by multiplying the mass (m) of the can by the acceleration due to gravity (g).
- Distance is the vertical displacement of the can, which is the height it is lifted or lowered.
- Theta is the angle between the force vector and displacement vector. Since the force and displacement are in the same direction here, theta is 0 degrees, and cos(0) = 1.
Let's calculate the work for each part:
Part A:
Given:
Mass of the can (m) = 3.2 kg
Height (d) = 1.4 m
First, we calculate the weight:
Weight (W) = mass (m) x acceleration due to gravity (g)
= 3.2 kg x 9.8 m/s^2
= 31.36 N
Now, we can calculate the work:
Work (W) = force (F) x distance (d) x cos(theta)
= Weight (W) x distance (d) x cos(0)
= 31.36 N x 1.4 m x 1
= 43.9 J (rounded to two significant figures)
Therefore, the work done on the can of paint in Part A is 43.9 Joules.
Part B:
Since the can is held stationary for half a minute, there is no vertical displacement (distance = 0). Therefore, no work is being done on the can during this time. The work done is 0 Joules.
Part C:
To find the work done during the lowering of the can, we use the same formula as in Part A, but now the distance is negative (since we are lowering the can).
Given:
Weight of the can (W) = 31.36 N
Height (d) = -1.4 m
Work (W) = force (F) x distance (d) x cos(theta)
= weight (W) x distance (d) x cos(0)
= 31.36 N x -1.4 m x 1
= -43.9 J (rounded to two significant figures)
Therefore, the work done on the can of paint when it is lowered in Part C is -43.9 Joules. The negative value indicates that the work is done by the gravitational force as the can moves in the direction opposing the gravitational force.