Question

If the block is moving at a constant velocity, then which of the following is a true statement? (A) The pulling force must be greater than the frictional force, but the weight of the object is equal to the normal reaction force. (B) The pulling force must be greater than the frictional force, and the weight of the object is greater than the normal reaction force. (C) The pulling force must be equal to the frictional force, and the weight of the object is equal to the normal reaction force. (D) The pulling force must be equal to the frictional force, but the weight of the object is less than the normal reaction force.

Short answer

(C) The pulling force must be equal to the frictional force, and the weight of the object is equal to the normal reaction force.

Step-by-step solution

Statement A: Pulling force > frictional force, weight = normal force

According to Newton's first law, if an object is in a state of constant velocity, it is subjected to interaction from opposite forces that are balanced. In this case, the pulling force must be equal to the frictional force, not greater than it. So, statement (A) is incorrect.

Statement B: Pulling force > frictional force, weight > normal force

Similarly, this statement suggests the pulling force must be greater than the frictional force, which contradicts Newton's first law. Moreover, in a horizontal motion, the weight of the object is always equal to the normal reaction force. So, statement (B) is incorrect.

Statement C: Pulling force = frictional force, weight = normal force

This statement aligns with Newton's first law, stating that the pulling force equals the frictional force, which causes the object to move at a constant velocity. It also correctly states that the weight of the object is equal to the normal reaction force in horizontal motion. Therefore, statement (C) is correct.

Statement D: Pulling force = frictional force, weight < normal force

This statement correctly states that the pulling force equals the frictional force. However, it incorrectly states that the weight of the object is less than the normal reaction force. In horizontal motion, the weight is always equal to the normal reaction force. So, statement (D) is incorrect. Based on the analysis, the correct answer is: (C) The pulling force must be equal to the frictional force, and the weight of the object is equal to the normal reaction force.

Key concepts

Constant Velocity

When an object moves with constant velocity, it means that there is no change in its speed or direction. This is a fundamental concept of Newton's First Law of Motion, which states that an object in motion will remain in motion at a constant velocity unless acted upon by an external force.

For constant velocity to occur, all the forces acting on the object must balance each other out. This means that the net force is zero.

• The pulling force must be equal to the frictional force.
• There is no net acceleration because the forces are in equilibrium.

Therefore, when dealing with problems involving constant velocity, always check the balance of forces involved.

Frictional Force

Frictional force is the force that resists the relative motion of two surfaces in contact. It plays a crucial role in determining how objects move.

In scenarios where an object is moving with a constant velocity, the pulling force is equal to the frictional force. This is because friction tries to slow down or stop the motion, but the pulling force counteracts it in equal measure.

• Friction depends on the nature of the surfaces in contact.
• It is usually proportional to the normal force acting on the object.

Understanding how friction works helps in analyzing and predicting the motion of objects on various surfaces.

Normal Reaction Force

The normal reaction force is the force exerted by a surface in a direction perpendicular to the surface. It balances the weight of an object resting on that surface.

When an object is moving horizontally at a constant velocity, the weight of the object (the force due to gravity) is equal to the normal reaction force. This relationship helps maintain equilibrium in the vertical direction.

• The normal force ensures that the object doesn't accelerate downward.
• It acts at a 90-degree angle to the surface.

Recognizing how the normal reaction force works will aid in setting up equations to solve for unknown forces or predicting how objects will interact with different surfaces.