A lawn roller is pushed across a lawn by a force of 103 N along the direction of the handle, which is 22.5° above the horizontal. If 63.0 W of power is developed for 90.0 s, what distance is the roller pushed?
To calculate the distance the roller is pushed, we need to use the formula for power:
Power = Work / Time
The work done is equal to the force exerted multiplied by the distance moved in the direction of the force:
Work = Force * Distance * cos(theta)
Where theta is the angle between the force and the direction of motion. In this case, theta is given as 22.5°.
Let's calculate the work done:
Work = Force * Distance * cos(theta)
63.0 W * 90.0 s = 103 N * Distance * cos(22.5°)
We can rearrange the equation to solve for the distance:
Distance = (Power * Time) / (Force * cos(theta))
Now we can substitute the given values into the equation:
Distance = (63.0 W * 90.0 s) / (103 N * cos(22.5°))
Using a calculator:
Distance ≈ 134.72 meters
Therefore, the roller is pushed approximately 134.72 meters.
To find the distance the roller is pushed, we can use the formula:
Distance = (Power × Time) / Force
First, let's convert the power from watts to joules per second (J/s) since the unit of power is given in watts. Since 1 watt is equal to 1 joule per second, the power is already in joules per second.
Now, we can substitute the given values into the formula:
Distance = (63.0 J/s × 90.0 s) / 103 N
Calculating this expression will give us the distance in meters. Let's do the math:
Distance = (5670 J) / 103 N
Distance ≈ 55.05 meters
Therefore, the roller is pushed approximately 55.05 meters.
P = 63.0 Watts = 63.0 J/s.
P = 103*cos22.5 * d/90 = 63 Watts/s
103*cos22.5 * d/90 = 63
103*cos22.5 * d = 63*90 = 5670
d = 5670/103*cos22.5 = 51 m.