A lawn roller is rolled across a lawn by a force
of 109 N along the direction of the handle,
which is 24.2� above the horizontal.
If the lawn roller develops 66.1 W of power
for 64 s, what distance is the roller pushed?
Answer in units of m.
To find the distance the lawn roller is pushed, we need to use the formula:
Work (W) = Power (P) × Time (t)
We are given the power (P) as 66.1 W and the time (t) as 64 s. Rearranging the formula, we can solve for work:
Work (W) = Power (P) × Time (t)
Work (W) = 66.1 W × 64 s
Now, let's calculate the work done by the lawn roller:
Work (W) = 66.1 W × 64 s
= 4230.4 J (Joules)
Since the force applied is along the direction of the handle and at an angle of 24.2 degrees above the horizontal, we need to consider only the horizontal component of the force. The horizontal component of the force can be calculated using the formula:
Force (F_horizontal) = Force (F) × cos(angle)
Considering the given force of 109 N and the angle of 24.2 degrees:
Force (F_horizontal) = 109 N × cos(24.2 degrees)
Now, let's calculate the horizontal component of the force:
Force (F_horizontal) = 109 N × cos(24.2 degrees)
= 98.52 N
The work done (W) is equal to the force times the distance (d):
Work (W) = Force (F_horizontal) × distance (d)
Rearranging the formula, we can solve for the distance:
distance (d) = Work (W) / Force (F_horizontal)
Now, let's calculate the distance the lawn roller is pushed:
distance (d) = 4230.4 J / 98.52 N
≈ 42.98 m
Therefore, the roller is pushed a distance of approximately 42.98 meters.
F cos24.2 * X = work done
= 66.1W*64s
= 4320 J
X = 4320/(Fcos24.2)
= 4320/99.42
= 43.5 m