A garden roller is kept at rest on a slope that makes an angle of 30 degrees the horizontal by an upward force of 2 500N parallel to the slope.
1. Calculate the mass of the roller?
2. Determine the magnitude of the force exerted by the surface on the roller?
1. M*g = Wt. of roller.
Fp = Mg*sin 30 = 2500
Mg = 2500/sin 30 = 5000 N.
M = 5000/g = 5000/9.8 = 510.2 kg
2. Fn = Mg*Cos 30 = 5000*Cos 30 = 4330 N
= Normal force = Force exerted by the
surface.
To calculate the mass of the roller, we can use the formula relating force, mass, and acceleration:
Force = mass * acceleration
In this case, the roller is kept at rest, so its acceleration is zero. The upward force exerted by the roller is 2,500N.
1. To find the mass of the roller, we can rearrange the formula as follows:
mass = force / acceleration
Since the acceleration is 0, the mass will be undefined (or infinite) if we use this formula directly. However, we can use the force component perpendicular to the slope to find the mass.
The force component perpendicular to the slope can be given by:
Force perpendicular = Force * sin(theta)
where theta is the angle between the slope and the horizontal.
In this case, theta = 30 degrees.
Force perpendicular = 2,500N * sin(30) = 2,500N * 0.5 = 1,250N
So, the force exerted by the surface on the roller (perpendicular to the slope) is 1,250N.
2. The magnitude of the force exerted by the surface on the roller (parallel to the slope) can be found by using the force component parallel to the slope. This can be given by:
Force parallel = Force * cos(theta)
Force parallel = 2,500N * cos(30) = 2,500N * 0.866 = 2,165N
Therefore, the magnitude of the force exerted by the surface on the roller (parallel to the slope) is 2,165N.