A 4.7 kg bag of groceries is in equilibrium on an incline of 26 degree. The acceleration of gravity is 9.81 m/s square. What is the magnitude of the normal force on the bag? Answer in units of N
F incline= mg sin θ
F incline = (4.7 kg) (9.81 m/s^2) sin (26)
F incline = 20.21 N = 21 N
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To find the magnitude of the normal force on the bag, we need to analyze the forces acting on it.
In this scenario, there are two main forces acting on the bag:
1. The force of gravity (mg): This is the weight of the bag, which is equal to the mass (m) of the bag multiplied by the acceleration due to gravity (g).
2. The normal force (N): This is the perpendicular force exerted by the incline on the bag, which opposes the force of gravity and prevents the bag from sinking into the incline.
Since the bag is in equilibrium, the normal force (N) is equal in magnitude but opposite in direction to the force of gravity (mg).
Given:
Mass of the bag (m) = 4.7 kg
Incline angle (θ) = 26 degrees
Acceleration due to gravity (g) = 9.81 m/s^2
First, we need to determine the component of gravity that acts parallel to the incline. This component is given by mg sinθ, while the component perpendicular to the incline is mg cosθ.
Here, we are interested in the magnitude of the normal force, which is the component perpendicular to the incline. Therefore, we will use mg cosθ to calculate it.
Calculating the normal force:
Normal force (N) = mg cosθ
Substituting the given values:
N = (4.7 kg) * (9.81 m/s^2) * cos(26 degrees)
Using a calculator:
N ≈ 42.757 N
Therefore, the magnitude of the normal force on the bag is approximately 42.757 N.
To find the magnitude of the normal force on the bag, we need to consider the forces acting on it. The normal force is perpendicular to the incline and opposes the force applied by gravity.
The force applied by gravity can be determined using the formula:
force_gravity = mass * acceleration due to gravity
Given that the mass of the bag is 4.7 kg and the acceleration due to gravity is 9.81 m/s^2, we can calculate the force_gravity as:
force_gravity = 4.7 kg * 9.81 m/s^2
This yields a force_gravity of 46.107 N (rounded to three decimal places).
However, in this case, the bag is on an incline. The force of gravity can be divided into two components: the component perpendicular to the incline (the normal force) and the component parallel to the incline (the weight force along the incline).
The weight force along the incline can be calculated as:
force_parallel = force_gravity * sin(θ)
Here, θ is the angle of the incline (26 degrees). So, we can substitute the values and solve for force_parallel:
force_parallel = 46.107 N * sin(26°)
Calculating this, we find that force_parallel is approximately 19.682 N (rounded to three decimal places).
Since the bag is in equilibrium on the incline, the normal force is equal and opposite to the weight force along the incline. Hence, the magnitude of the normal force on the bag is also approximately 19.682 N.