A man using a 70 kg garden roller on a level surface exerts a force 20 kgf at 45 degrees to the ground . Find the vertical force of the roller on the ground if he ;
a) pulls the roller.
b) pushes the roller.
To find the vertical force of the roller on the ground when it is being pulled or pushed, we need to decompose the applied force into its horizontal and vertical components.
Let's start with the given information:
- Mass of the garden roller (m) = 70 kg
- Applied force (F) = 20 kgf (a kilogram-force is a unit of force in the gravitational metric system, where 1 kgf = 9.81 N)
- Angle of the applied force (θ) = 45 degrees
a) When the roller is being pulled:
In this case, the applied force is directed upwards at a 45-degree angle to the ground. We need to determine the vertical force component (F_vertical) to find the force exerted by the roller on the ground.
To find F_vertical, we can use trigonometry. The vertical force component can be found using the equation:
F_vertical = F * sin(θ)
Substituting the values:
F = 20 kgf = 20 * 9.81 N = 196.2 N (converting kgf to N)
θ = 45 degrees
F_vertical = 196.2 N * sin(45 degrees) ≈ 196.2 N * 0.707 ≈ 138.6 N
Therefore, when the roller is being pulled, the vertical force exerted by the roller on the ground is approximately 138.6 Newtons.
b) When the roller is being pushed:
In this case, the applied force is directed downwards at a 45-degree angle to the ground. We use the same equation as above to find the vertical force exerted by the roller on the ground.
Using the same values:
F = 20 kgf = 196.2 N
θ = 45 degrees
F_vertical = 196.2 N * sin(45 degrees) ≈ 196.2 N * 0.707 ≈ 138.6 N
Therefore, when the roller is being pushed, the vertical force exerted by the roller on the ground is also approximately 138.6 Newtons.
To find the vertical force of the roller on the ground, we can use trigonometry.
a) To find the vertical force if the man pulls the roller, we need to find the component of the force vector that is perpendicular to the ground.
Given:
Mass of the garden roller (m) = 70 kg
Force exerted by the man (F) = 20 kgf
Angle of the force vector with respect to the ground (θ) = 45 degrees
First, we need to convert the force from kilograms-force (kgf) to Newtons (N) since the SI unit for force is Newton.
1 kgf = 9.81 N
So, converting F to Newtons:
F = 20 kgf * 9.81 N/kgf = 196.2 N
Now, we can find the vertical force (Fv) by using the equation:
Fv = F * sin(θ)
Fv = 196.2 N * sin(45 degrees)
Fv = 196.2 N * 0.7071
Fv ≈ 138.59 N
Therefore, when the man pulls the roller, the vertical force of the roller on the ground is approximately 138.59 N.
b) To find the vertical force if the man pushes the roller, we use a similar process.
Again, the force (F) is the same as before: F = 196.2 N.
This time, however, we need to find the component of the force vector that is parallel to the ground. In this case, it will be the cosine of the angle:
Fh = F * cos(θ)
Fh = 196.2 N * cos(45 degrees)
Fh = 196.2 N * 0.7071
Fh ≈ 138.59 N
Therefore, when the man pushes the roller, the vertical force of the roller on the ground is approximately 138.59 N.
a) 70 - 20 cos45 = 55.9 kgf
b) 70 + 20 cos45 = 84.1 kgf
1 kgf = 9.8 N = 2.2 lbf
The use of kgf (kilograms of force) units is usually discouraged in physics. The preferred force/weight unit is the Newton.