A 5.6 kg bag of groceries is in equilibrium on
an incline of 32�.
The acceleration of gravity is 9.81 m/s2 . What is the magnitude of the normal force
on the bag?
Well, isn't it funny how groceries always seem to find themselves in exciting situations? So, to solve this problem, we'll need to consider the forces acting on the bag.
First, we have the force of gravity pulling it downwards. This force can be calculated using the formula:
force of gravity = mass x acceleration due to gravity
In this case, the mass is 5.6 kg and the acceleration due to gravity is 9.81 m/s^2. So, the force of gravity is:
force of gravity = 5.6 kg x 9.81 m/s^2 ≈ 54.936 N
Now, since the bag is on an incline, there is an upward force called the normal force that keeps the bag from sinking into the surface. The normal force acts perpendicular to the incline. To find the magnitude of the normal force, we need to use trigonometry.
The normal force can be given by the equation:
normal force = force of gravity x cosine of the angle of incline
In this case, the angle of incline is 32 degrees. So, the magnitude of the normal force is:
normal force = 54.936 N x cos(32 degrees) ≈ 46.415 N
So, the magnitude of the normal force on the bag is approximately 46.415 N. And remember, folks, gravity may bring us down, but a good laugh can always lift our spirits!
To find the magnitude of the normal force on the bag, we need to consider the forces acting on it.
1. Weight force (downwards): This force is given by the formula Fg = m * g, where m is the mass of the bag (5.6 kg) and g is the acceleration due to gravity (9.81 m/s²). Therefore, the weight force is Fg = 5.6 kg * 9.81 m/s².
2. Force component parallel to the incline: Since the bag is in equilibrium, the net force in the direction parallel to the incline is zero. Therefore, the force component parallel to the incline is canceled out.
3. Force component perpendicular to the incline (normal force): The normal force is responsible for canceling out the force component perpendicular to the incline. Since the bag is in equilibrium, this force is equal in magnitude to the weight force.
So, the magnitude of the normal force on the bag is equal to the weight force, which is Fg = 5.6 kg * 9.81 m/s².
To find the magnitude of the normal force on the bag, we need to consider the forces acting on the bag in equilibrium.
In this case, the bag is on an incline, so there are two main forces acting on it: the gravitational force (weight) pulling it downward and the normal force pushing it perpendicular to the incline.
The weight of the bag can be calculated using the equation:
Weight = mass * acceleration due to gravity
Weight = 5.6 kg * 9.81 m/s^2 (acceleration due to gravity)
Weight = 54.936 N (rounded to three decimal places)
Since the bag is in equilibrium, the weight and the normal force are equal in magnitude but act in opposite directions. Therefore, the magnitude of the normal force is also 54.936 N.