A man pulls a lawnmower with a mass of 50 kilogram accross a lawn, its pulling force is 400 newtons at angle of 50 degrees with a horizontal line.(a) resolve the force into two components , one parallel to the ground and one perpendicular to the ground .(b) explain why it is easier to pull the lawnmower than to push it.
(A) the force parallel to the ground is 400 cos50.
The force perpendicular to the ground is 400 sin50..
(B) When pulling the lawnmower, the upward applied force opposes t he weight force. This has the effect of reducing the friction force.
(a) To resolve the pulling force into two components, one parallel (F_parallel) and one perpendicular (F_perpendicular) to the ground, we can use trigonometry.
Using the given information:
Pulling force (F) = 400 newtons
Angle (θ) = 50 degrees
1. Calculate the parallel component:
F_parallel = F * cos(θ)
F_parallel = 400 N * cos(50°)
F_parallel ≈ 400 N * 0.643
F_parallel ≈ 257.2 N
2. Calculate the perpendicular component:
F_perpendicular = F * sin(θ)
F_perpendicular = 400 N * sin(50°)
F_perpendicular ≈ 400 N * 0.766
F_perpendicular ≈ 306.4 N
So, the lawnmower experiences a parallel force of approximately 257.2 newtons and a perpendicular force of approximately 306.4 newtons.
(b) It is easier to pull the lawnmower than to push it because when pulling, the parallel force helps to overcome the friction between the lawnmower's wheels and the ground. The parallel force helps in propelling the lawnmower forward while reducing the frictional resistance. On the other hand, when pushing, the parallel force acts against the friction, making it harder to move the lawnmower. Additionally, when pushing, the weight of the lawnmower acts as a downward force, further increasing the resistance to motion. Therefore, pushing requires more force and effort compared to pulling.