 # The resultant force equation

3 questions about The resultant force equation

1. A car with a mass of 5 tonnes moves from rest in 50 seconds, reaching a speed of 72 km/hour. The force on the car is…

Known:

Mass (m) = 5 tons = 5000 kg

Initial speed (vo) = 0

Final speed (vt) = 72 km/h = 20 m/s

Time interval (t) = 50 seconds

Wanted: Force (F)

Solution:

Calculate the acceleration using the Non Uniform Linear Motion formula:

vt = vo + a t

20 = 0 + a (50)

20 = 50 a

a = 20 / 50 = 0,4 m/s2

Calculate the resultant force using Newton’s second law formula:

ΣF = m a

F = (5000)(0,4) = 2000 Newton

2. A car has a mass of 1 ton, for 4 seconds its speed increases uniformly from 10 m/s to 18 m/s. Determine the magnitude of the force that accelerates the car.

Known:

The mass of the car (m) = 1 ton = 1000 kg

Time interval (t) = 4 seconds

Initial velocity (vo) = 10 m/s

Final velocity (vt) = 18 m/s

Wanted: Force (F)

Solution:

Calculate the acceleration using the Non Uniform Linear Motion formula:

vt = vo + a t

18 = 10 + a (4)

18 – 10 = a (4)

8 = 4 a

a = 8 / 4 = 2 m/s2

Calculate the resultant force using Newton’s second law formula:

ΣF = m a

F = (1000)(2) = 2000 Newton

3. The two force vectors are perpendicular to each other which results in a resultant of 10 N. If one of the force vectors is 6 N , determine the magnitude of the other force vector.

Known:

Resultant force (F) = 10 N

Force 1 (F1) = 6 N

Wanted: Force 2 (F2)

Solution:

F2 = 10 – 6 = 4 Newton

20 conceptual questions and answers related to force and the resultant force.

1. Question: What is force? Answer: A force is a push or pull upon an object resulting from the object’s interaction with another object.
2. Question: What is the unit of force? Answer: The SI unit of force is the Newton (N), which is equivalent to 1 kg x m/s².
3. Question: What is resultant force? Answer: Resultant force is the single force which can replace the effect of a number of individual forces acting on a body.
4. Question: How is resultant force calculated when two or more forces act on a body? Answer: If the forces are acting along the same line, the resultant force can be found by adding or subtracting the forces. For forces not acting along the same line, vector addition methods are used.
5. Question: What happens when the resultant force on a body is zero? Answer: If the resultant force on a body is zero, the body will remain at rest if it is at rest, or continue to move at a constant velocity if it is in motion. This is a direct consequence of Newton’s first law of motion.
6. Question: Can a body move if the resultant force on it is zero? Answer: Yes, a body can move even if the resultant force on it is zero. It will move with a constant velocity. This is because a zero resultant force means there’s no acceleration, not necessarily no motion.
7. Question: What is the difference between contact and non-contact forces? Answer: Contact forces require physical contact between two objects, like friction or tension. Non-contact forces act at a distance, like gravity or electromagnetic forces.
8. Question: How does the resultant force affect the motion of an object? Answer: The resultant force determines the acceleration of an object. According to Newton’s second law, acceleration is directly proportional to the resultant force and inversely proportional to the mass of the object.
9. Question: What is the resultant force on a body moving with constant velocity? Answer: If a body is moving with a constant velocity, the resultant force on the body is zero. This is because there is no acceleration, and by Newton’s second law, force is equal to mass times acceleration.
10. Question: How is the direction of the resultant force related to the direction of motion? Answer: The direction of the resultant force determines the direction of acceleration, not necessarily the direction of motion. If an object is moving and the resultant force is in the same direction, the object will speed up. If the resultant force is in the opposite direction, the object will slow down.
11. Question: What is the difference between weight and force? Answer: Weight is a specific type of force. It is the force exerted on an object due to gravity.
12. Question: What is net force? Answer: Net force is another term for resultant force. It’s the vector sum of all the forces acting on an object.
13. Question: Can the resultant force be less than the magnitude of the individual forces? Answer: Yes, the resultant force can be less than the magnitude of the individual forces, especially when the forces are acting in opposite directions.
14. Question: What does it mean when the forces on a body are balanced? Answer: Balanced forces mean that the resultant force on the body is zero. In this case, the body will not accelerate and will either remain at rest or move with a constant velocity.
15. Question: How is the force of gravity related to the resultant force on a falling object? Answer: For a falling object in a vacuum, the force of gravity is the resultant force as there are no other forces acting. If there’s air resistance, the resultant force is the force of gravity minus the air resistance.
16. Question: What is the effect of the resultant force on the kinetic energy of an object? Answer: If the resultant force is not zero, it will cause an acceleration, which will change the velocity of the object, and therefore, its kinetic energy.
17. Question: What is the difference between normal force and the resultant force? Answer: The normal force is the force exerted by a surface to support the weight of an object resting on it, and it acts perpendicular to the surface. The resultant force is the vector sum of all the forces acting on an object, including the normal force if applicable.
18. Question: What does it mean if the resultant force on an object in motion is zero? Answer: If the resultant force on an object in motion is zero, it means the object will continue to move with a constant velocity. This could mean moving in a straight line at a constant speed, or remaining still.
19. Question: How do the individual forces and the resultant force relate to motion in a circular path? Answer: For an object to move in a circular path, the resultant force must be directed towards the center of the circle. This resultant force is often referred to as the centripetal force.
20. Question: Can there be motion in the direction perpendicular to the resultant force? Answer: Yes, there can be motion in a direction perpendicular to the resultant force. For example, an object in uniform circular motion moves perpendicular to the resultant (centripetal) force.