Math Problem Statement

A 20-kg crate (m = 20 kg, F_grav = 200 N) is being pulled at constant velocity to the right across a frictional horizontal surface by a 50-N force.

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 Fgrav=200NF_{\text{grav}} = 200 \, \text{N}. 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, m=20kgm = 20 \, \text{kg}
  • Gravitational force, Fgrav=200NF_{\text{grav}} = 200 \, \text{N}
  • Applied force to the right, Fapplied=50NF_{\text{applied}} = 50 \, \text{N}
  • The crate is moving at constant velocity (implying equilibrium, where the net force is zero).

1. Understanding Forces:

  • Weight (Gravitational force): The weight is Fgrav=mg=20kg×9.8m/s2=196NF_{\text{grav}} = m \cdot g = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N}, which is approximately 200 N.
  • Normal Force (Upward reaction from the surface): Since there is no vertical movement, the normal force FnormalF_{\text{normal}} is equal to the gravitational force, which is 200N200 \, \text{N}.
  • Frictional Force: Since the crate moves with constant velocity, the applied force (50 N) is balanced by the frictional force. Therefore, the frictional force Ffriction=50NF_{\text{friction}} = 50 \, \text{N}.

2. Net Force:

Since the velocity is constant, the net force on the crate is zero. All forces (horizontal and vertical) are in equilibrium: Fnet=0F_{\text{net}} = 0

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:

  1. How do you calculate the coefficient of friction in this scenario?
  2. What would happen if the applied force was increased to 60 N?
  3. How would the net force change if the crate were on an incline instead of a horizontal surface?
  4. What role does the normal force play in determining the frictional force?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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