A man using a 70 kg garden roller on a level surface, exert a force of 200 newton at 45 angle to the ground. Find the vertical force of the roller on the ground (a) if he pulls
(b) if he pushes the roller
To find the vertical force of the roller on the ground, we need to resolve the force into its horizontal and vertical components.
(a) When the man pulls the roller:
The vertical force of the roller on the ground will be equal to the component of the applied force that acts vertically downward.
First, let's find the vertical component of the applied force:
Vertical component = Force × sin(angle)
Vertical component = 200 N × sin(45°)
Using trigonometric calculations, we can find that sin(45°) is equal to √2/2.
Vertical component = 200 N × (√2/2)
Vertical component = 200 N × 0.707
Vertical component = 141.4 N
Therefore, when the man pulls the roller, the vertical force of the roller on the ground is 141.4 Newtons.
(b) When the man pushes the roller:
Since the force is already applied at an angle to the ground, we can simply find the vertical component of the applied force.
The vertical force of the roller on the ground will be equal to the component of the applied force that acts vertically downward.
To find the vertical component of the applied force when pushing, we use the same formula:
Vertical component = Force × sin(angle)
Vertical component = 200 N × sin(45°)
Using trigonometric calculations, we can again find that sin(45°) is equal to √2/2.
Vertical component = 200 N × (√2/2)
Vertical component = 200 N × 0.707
Vertical component = 141.4 N
Therefore, when the man pushes the roller, the vertical force of the roller on the ground is 141.4 Newtons, which is the same as when he pulls it.
a) forcedownward= mg-200*.707
= 70*9.8-200*.707=545N
b) force downward=mg+200*.707=827N