Math Problem Statement
Solution
The image presents a physics problem where a 20-kg crate is pulled with a force of 50 N across a horizontal surface with a gravitational force of . The crate is moving at constant velocity, which indicates that the forces are balanced (there is no net acceleration).
Step-by-Step Solution:
Given:
- Mass of the crate,
- Gravitational force,
- Applied force to the right,
- The crate is moving at constant velocity (implying equilibrium, where the net force is zero).
1. Understanding Forces:
- Weight (Gravitational force): The weight is , which is approximately 200 N.
- Normal Force (Upward reaction from the surface): Since there is no vertical movement, the normal force is equal to the gravitational force, which is .
- Frictional Force: Since the crate moves with constant velocity, the applied force (50 N) is balanced by the frictional force. Therefore, the frictional force .
2. Net Force:
Since the velocity is constant, the net force on the crate is zero. All forces (horizontal and vertical) are in equilibrium:
This happens because the applied force is perfectly counteracted by the frictional force, and there is no net vertical motion (normal force equals gravitational force).
Answer:
The net force on the crate is 0 N.
Would you like more details or further clarification on any part of this problem?
5 Related Questions:
- How do you calculate the coefficient of friction in this scenario?
- What would happen if the applied force was increased to 60 N?
- How would the net force change if the crate were on an incline instead of a horizontal surface?
- What role does the normal force play in determining the frictional force?
- How can we calculate the acceleration if the applied force were not balanced by friction?
Tip:
When objects move at a constant velocity, the forces acting on them are in equilibrium. This means the net force is zero, and it's a useful clue for solving similar problems.
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Math Problem Analysis
Mathematical Concepts
Forces and Equilibrium
Newton's Laws
Friction
Formulas
F_grav = m * g
F_net = F_applied - F_friction
F_net = 0 (at constant velocity)
Theorems
Newton's First Law of Motion (Inertia)
Equilibrium of forces
Suitable Grade Level
Grades 9-11
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