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) m g = 9.81 * 4.5 = 44.15 N
(b) 44.15 cos 12
(c) 44.15 cos 25
(d) what else is new?
To determine the normal force acting on a laundry basket in each of the given situations, we can make use of Newton's second law of motion:
ΣF = ma
where ΣF represents the sum of all forces acting on the object, m is the mass of the object, and a is the acceleration of the object. In situations (a), (b), (c), and (d), we assume that the laundry basket is at rest, meaning its acceleration is zero. Therefore, the sum of all forces acting on the basket must also be zero.
(a) At rest on a horizontal surface:
When the laundry basket is at rest on a horizontal surface, the only vertical force acting on it is the gravitational force (weight) pulling it downward. According to Newton's third law of motion, the normal force is equal in magnitude but opposite in direction to the force exerted by the weight. Since the basket is at rest, the normal force and weight must balance each other.
So, the normal force in this case is equal to the weight of the basket, which can be calculated using the equation:
weight = mass * acceleration due to gravity (g)
where g is approximately 9.8 m/s^2.
Plugging in the given mass of the laundry basket (4.5 kg), the normal force can be calculated as:
normal force = weight = mass * g = 4.5 kg * 9.8 m/s^2 = 44.1 N
Therefore, the normal force for a laundry basket at rest on a horizontal surface is 44.1 Newtons (N).
(b) At rest on a ramp inclined at 12° above the horizontal:
In this situation, the weight of the laundry basket can be divided into two components: a component perpendicular to the incline (normal force) and a component parallel to the incline (force due to gravity pulling the basket down the ramp). The normal force will act perpendicular to the incline and counteract the component of weight pulling the basket into the ramp.
To calculate the normal force, we need to determine the vertical and horizontal components of weight. The vertical component is given by:
vertical component of weight = weight * cos(12°)
And the horizontal component of weight is given by:
horizontal component of weight = weight * sin(12°)
Since the basket is at rest, the vertical component of weight should be equal to the normal force. Therefore,
normal force = vertical component of weight = weight * cos(12°)
Substituting the value for weight, we get:
normal force = (mass * g) * cos(12°)
Plugging in the given mass of the laundry basket (4.5 kg) and the value of g (9.8 m/s^2), we can calculate the normal force:
normal force = (4.5 kg * 9.8 m/s^2) * cos(12°) ≈ 41.2 N
Therefore, the normal force for a laundry basket at rest on a ramp inclined at 12° above the horizontal is approximately 41.2 Newtons (N).
(c) At rest on a ramp inclined at 25° above the horizontal:
The calculation for this situation is similar to part (b). We need to determine the vertical and horizontal components of the weight of the basket and find the normal force, which is equal to the vertical component.
normal force = vertical component of weight = weight * cos(25°)
Substituting the value for weight, we get:
normal force = (mass * g) * cos(25°)
Plugging in the given mass of the laundry basket (4.5 kg) and the value of g (9.8 m/s^2), we can calculate the normal force:
normal force = (4.5 kg * 9.8 m/s^2) * cos(25°) ≈ 39.5 N
Therefore, the normal force for a laundry basket at rest on a ramp inclined at 25° above the horizontal is approximately 39.5 Newtons (N).
(d) At rest on a ramp inclined at 45° above the horizontal:
Again, the calculation for this situation is similar to parts (b) and (c). We need to determine the vertical and horizontal components of the weight of the basket and find the normal force, which is equal to the vertical component.
normal force = vertical component of weight = weight * cos(45°)
Substituting the value for weight, we get:
normal force = (mass * g) * cos(45°)
Plugging in the given mass of the laundry basket (4.5 kg) and the value of g (9.8 m/s^2), we can calculate the normal force:
normal force = (4.5 kg * 9.8 m/s^2) * cos(45°) ≈ 31.4 N
Therefore, the normal force for a laundry basket at rest on a ramp inclined at 45° above the horizontal is approximately 31.4 Newtons (N).