a passenger at an airport pulls a rolling suitcase by its handle. If the force used is 10N and the handle makes an angle of 25 degrees to the horizontal, what is the work done by the pulling force while the passenger walks 200m?
Fh = hor = 10cos25 = 9.06N.
W = Fh * d = 9.06 * 200 = 1812.6.
To calculate the work done by the pulling force, we need to use the formula:
Work = Force x Distance x cos(angle)
In this case, the force used is 10N, the distance is 200m, and the angle is 25 degrees.
First, we need to convert the angle from degrees to radians:
Angle in radians = Angle in degrees x π / 180
= 25° x π / 180
= 0.4363 radians (rounded to four decimal places)
Now, we can calculate the work by substituting the values into the formula:
Work = 10N x 200m x cos(0.4363 radians)
Using a calculator, we find:
Work ≈ 10N x 200m x 0.901
≈ 1802 J (rounded to three significant figures)
Therefore, the work done by the pulling force while the passenger walks 200m is approximately 1802 Joules.
To calculate the work done by the pulling force, we can use the formula:
Work = Force * Distance * Cosine(theta)
Where:
- Work is the work done by the force (in Joules),
- Force is the magnitude of the force applied (in Newtons),
- Distance is the distance traveled in the direction of the force (in meters),
- Theta is the angle between the force and the direction of motion (in degrees).
In this case, the force applied is 10N, the distance traveled is 200m, and the angle is 25 degrees. We need to convert the angle to radians before using it in the formula.
First, let's convert the angle to radians:
theta_radians = 25 degrees * (pi / 180 degrees)
Now, we can calculate the work:
Work = 10N * 200m * Cosine(25 degrees)
= 10N * 200m * Cosine(theta_radians)
To find the value of Cosine(theta_radians), we can use a scientific calculator or an online tool.
Finally, we can substitute the values and calculate the work.