Question

A man, using a $70kg$ garden roller on a level surface exerts a force of $200N$ at $45^\circ$ to the ground. What is the vertical force of the roller on the ground, if he pushes the roller? $\left( {g = 10{\text{ }}m{s^{ - 1}}} \right)$

Answer 1

When an object collides with a surface, the usual force acts perpendicular to the surface and is proportional to the perpendicular part of the object's weight. On a flat table (horizontal), the usual force vertical equals the weight of the material (mg).

Complete step by step answer:
Given, Mass of the roller = $70kg$
Force exerted = $200N$
Angle the force makes with the ground $\phi = 45^\circ$

Weight of the roller $W = mg$
Where, $g$ is the acceleration due to gravity = $9.81m/{s^2}$
Thus, weight of the roller $= 70{\text{ }} \times {\text{ }}9.81 = 686.7{\text{ }}N$
The effective vertical force exerted by the man
$F = {\text{ }}F{\text{ }}sin\phi$
$\Rightarrow F = 200{\text{ }}sin{\text{ }}45^\circ$
$\Rightarrow F = 200{\text{ }} \times 0.707 = 141.5{\text{ }}N$

(i) If the man pulls, then the exerted force will be in opposite direction to the weight of the roller vertically upwards
Resultant vertical force = $686.7{\text{ }}N - 141.5{\text{ }}N = \;545.2N$ upwards

(ii) If he pushes, then the exerted force will be in the direction of the weight vertically downwards.
Resultant vertical force = $686.7{\text{ }}N + 141.5{\text{ }}N = \;828.2N$ downwards

Note: Vertical Force is a $1995$ vertical-scrolling shooter video game developed by Hudson Soft in Japan and released by Nintendo in North America for the Virtual Boy. The player pilots the Ragnarok, a starship that must kill a malfunctioning supercomputer on a human colony planet before humanity is wiped out. The normal force behaves perpendicular to the contact surface at all times. It has the ability to act in opposition to gravity or some other force that forces an object against a surface.