Determine the normal force for a laundry basket with a mass of 4.5 kg in each of the following situations...
(a) at rest on a horizontal surface? ___ N
(b) at rest on a ramp inclined at 12° above the horizontal? ___ N
(c) at rest on a ramp inclined at 25° above the horizontal? ___ N
(d) at rest on a ramp inclined at 45° above the horizontal? ____ N
a) Fn =mg
b) c) d) Fn = mg cos(theta)
To determine the normal force in each situation, we need to consider the forces acting on the laundry basket. The normal force is the force exerted by a surface to support an object resting on it. It acts perpendicular to the surface.
(a) When the laundry basket is at rest on a horizontal surface, there is no vertical acceleration. Therefore, the normal force is equal to the weight of the basket.
We can find the weight using the formula:
Weight = mass * acceleration due to gravity
In this case, the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 4.5 kg * 9.8 m/s^2 = 44.1 N
So, the normal force is also 44.1 N.
(b) When the laundry basket is at rest on a ramp inclined at 12° above the horizontal, we need to consider both the weight and the component of the weight perpendicular to the surface.
The component of the weight perpendicular to the surface can be found using the formula:
Weight perpendicular = Weight * cos(angle)
In this case, the angle is 12°.
Weight = 4.5 kg * 9.8 m/s^2 = 44.1 N
Weight perpendicular = 44.1 N * cos(12°) ≈ 43.53 N
So, the normal force is approximately 43.53 N.
(c) When the laundry basket is at rest on a ramp inclined at 25° above the horizontal, we once again need to consider both the weight and the component of the weight perpendicular to the surface.
Weight = 4.5 kg * 9.8 m/s^2 = 44.1 N
Weight perpendicular = 44.1 N * cos(25°) ≈ 39.88 N
So, the normal force is approximately 39.88 N.
(d) When the laundry basket is at rest on a ramp inclined at 45° above the horizontal, the angle is such that the normal force will equal the weight because the incline is steep enough that the weight fully acts perpendicular to the surface.
Weight = 4.5 kg * 9.8 m/s^2 = 44.1 N
So, the normal force is also 44.1 N.