Normal force equation

3 questions about Normal force equation

1. A block has a mass of 5 kg. If g = 10 m/s², determine:

a) the weight of the block

b) the normal force if the block is placed on a flat plane

c) the normal force if the block rests on an inclined plane that forms an angle of 30^o to the horizontal

Known:

The mass of the block (m) = 5 kg

Acceleration due to gravity (g) = 10 m/s²

Wanted: w, N on the plane and N on the incline

Solution:

a) Beam weight

w = m g = 5 (10) = 50 Newton

b) The normal force if the block is in a flat plane

N = w = 50 Newton

c) The normal force if the block is on an inclined plane

N = w_y = w cos θ = 50 (cos 30) = 50 (½ √3) = 25√3 Newton

2. A 120 gram eraser is pressed perpendicularly to the board with a force of 15 N. What is the normal force acting on the eraser?

Known:

Mass (m) = 120 grams = 0.12 kg

Force (F) = 15 Newton

Wanted: Normal force

Solution:

Normal force = thrust = 15 Newton

3. Bottled drinking water that is still in the box is pulled with a force of F = 200 N which forms an angle of 37^o with the horizontal. Sin 37^o = 0.6. The mass of the cardboard and its contents is 20 kg. If the coefficient of static friction on the floor is 0.5 and the coefficient of kinetic friction on the floor is 0.2, determine the normal force acting on the cardboard.

Known:

Pull force (F) = 200 N

Sin 37 = 0,6

Fy = F sin 37 = (200)(0,6) = 120 N

Cardboard mass (m) = 20 kg

The weight of the cardboard (w) = m g = (20)(10) = 200 N

Wanted: Normal force on cardboard (N)

Solution:

Calculate the normal force using the normal force formula:

N = w – F_y = 200 – 120 = 80 Newton

20 conceptual questions and answers related to normal force.

1. Question: What is normal force? Answer: Normal force is the force exerted by a surface that supports the weight of an object resting on it. It acts perpendicular (or “normal”) to the surface.
2. Question: How is normal force calculated on a flat surface? Answer: On a flat surface, the normal force is equal to the weight of the object. It can be calculated as N = mg, where m is the mass of the object and g is the acceleration due to gravity.
3. Question: Can normal force be zero? Answer: Yes, the normal force can be zero. This occurs when there’s no contact between the object and a surface (such as an object in free-fall), or when other vertical forces completely balance the object’s weight.
4. Question: How does the normal force change on an inclined plane? Answer: On an inclined plane, the normal force is less than the weight of the object because only a component of the weight acts perpendicular to the surface. It can be calculated as N = mgcosθ, where θ is the angle of the incline.
5. Question: How does the normal force relate to friction? Answer: The normal force plays a crucial role in calculating the force of friction. The frictional force is equal to the product of the coefficient of friction and the normal force (f = μN).
6. Question: Can the normal force be horizontal? Answer: Yes, the normal force can be horizontal if the surface providing the force is vertical.
7. Question: Is normal force always equal to weight? Answer: No, normal force isn’t always equal to weight. They are equal when an object is at rest or moving at constant velocity on a flat surface. However, in other situations (like on an inclined plane or during vertical acceleration), the normal force differs from weight.
8. Question: How does normal force change in an elevator? Answer: In an accelerating elevator moving upwards, the normal force is greater than the weight because it must counteract both the weight and the upward acceleration. In an elevator accelerating downwards, the normal force is less than the weight.
9. Question: Is normal force a reaction force? Answer: Yes, the normal force is a reaction force that surfaces exert to support the weight of objects resting on them, according to Newton’s third law of motion.
10. Question: Can the normal force do work on an object? Answer: The normal force does not do work on an object moving along a surface because it acts perpendicular to the direction of motion. Work is defined as the force multiplied by the distance an object moves in the direction of the force.
11. Question: Is normal force a vector quantity? Answer: Yes, normal force is a vector quantity. It has both magnitude and direction.
12. Question: How does the normal force change if the object’s mass doubles? Answer: If the object’s mass doubles, the normal force also doubles because the weight of the object (which the normal force counteracts) has doubled.
13. Question: How does the normal force change when an object is in free fall? Answer: When an object is in free fall, the normal force is zero because there is no surface to exert a supporting force.
14. Question: How does the normal force change with the angle of an inclined plane? Answer: As the angle of an inclined plane increases, the normal force decreases. This is because less of the object’s weight is directed perpendicular to the surface.
15. Question: Can there be a normal force in the absence of gravity? Answer: In the absence of gravity, an object doesn’t have weight, so a surface doesn’t need to exert a normal force to support it. However, a normal force can still exist due to other forces acting on the object.
16. Question: How is the normal force related to the net force on an object? Answer: For an object at rest or moving at a constant velocity, the net force is zero, so the upward normal force balances the downward force of gravity. If other forces are involved, the normal force can contribute to the net force.
17. Question: How does the normal force change if the coefficient of friction changes? Answer: The normal force is independent of the coefficient of friction. It doesn’t change when the coefficient of friction changes.
18. Question: How does the normal force affect the motion of an object? Answer: The normal force doesn’t cause an object’s motion, but it can affect the motion by determining the maximum possible frictional force, which can prevent or oppose motion.
19. Question: Is normal force conservative or nonconservative? Answer: Normal force is a nonconservative force because it doesn’t store energy that can be recovered later. Work done by the normal force generally goes into deforming the object or the surface, not changing the object’s kinetic or potential energy.

20. Question: Can there be a normal force without contact between the object and a surface? Answer: No, there can’t be a normal force without contact. Normal force is exerted by a surface on an object in contact with it. Without contact, there’s no normal force.