A 4.3 kg bag of groceries is in equilibrium on an incline of angle θ = 30°. Find the magnitude of the normal force on the bag.
M*g*cos30 = 36.5 Newtons
To find the magnitude of the normal force on the bag, we will use the concept of equilibrium and resolve the forces acting on the bag.
First, let's consider the forces acting on the bag on an inclined plane:
1. Weight: The weight of the bag acts vertically downwards. It is given by W = mg, where m is the mass of the bag and g is the acceleration due to gravity (approximately 9.8 m/s²).
2. Normal force: The normal force acts normal (perpendicular) to the incline, pushing the bag upwards. This force counteracts the component of the weight acting down the incline.
3. Friction: Although the question does not mention the presence of friction, we'll assume there is no friction in this problem unless otherwise stated.
To find the magnitude of the normal force, we need to resolve the weight of the bag into two components: one parallel to the incline (mg*sinθ), and one perpendicular to the incline (mg*cosθ).
Here's how you can calculate the magnitude of the normal force:
1. Calculate the weight of the bag by multiplying the mass (4.3 kg) by the acceleration due to gravity (9.8 m/s²):
Weight (W) = mass (m) * acceleration due to gravity (g)
W = 4.3 kg * 9.8 m/s²
2. Resolve the weight into two components:
Weight parallel to the incline (W_parallel) = Weight * sinθ
Weight perpendicular to the incline (W_perpendicular) = Weight * cosθ
3. The magnitude of the normal force (N) is equal to the weight perpendicular to the incline:
N = W_perpendicular
Using the above steps, you can now calculate the magnitude of the normal force by plugging in the values into the equations.