A person puts a suitcase of mass 10.9 kg into a van, moving the suitcase a total distance of 0.90 m: 0.60 m up and 0.30 m horizontally. How much work is done by the person?
To find the work done by the person, we can use the formula:
Work (W) = Force (F) × Distance (d) × cos(θ)
Where:
- Force (F) is the force applied to move the suitcase.
- Distance (d) is the total distance traveled by the suitcase.
- θ is the angle between the applied force and the direction of displacement.
In this case, we need to find the force applied by the person to move the suitcase, and then calculate the work.
First, let's find the vertical component of the applied force. The suitcase is moved up by a distance of 0.60 m, so we need to counteract the force of gravity pulling the suitcase downward.
The weight of the suitcase can be found by multiplying its mass (m) by the acceleration due to gravity (g):
Weight (W) = mass (m) × acceleration due to gravity (g)
Here, the mass of the suitcase is given as 10.9 kg, and the acceleration due to gravity is approximately 9.8 m/s^2:
Weight (W) = 10.9 kg × 9.8 m/s^2
Next, we calculate the vertical component of the applied force:
Vertical force = Weight × cos(θ)
θ = 0 degrees (since the vertical direction is opposite to the gravitational force)
Now let's calculate the horizontal component of the applied force. The suitcase is moved horizontally by a distance of 0.30 m, so we don't need to consider any vertical force here since the angle (θ) is 90 degrees.
Now that we have the vertical and horizontal components of the applied force, the total force can be found using the Pythagorean theorem:
Force = √(Vertical force^2 + Horizontal force^2)
Finally, we can calculate the work done by multiplying the force by the total distance traveled by the suitcase:
Work = Force × total distance (d)
By following these steps, you can find the work done by the person putting the suitcase into the van.