To find the force of friction acting on the iron sphere, we can use the work-energy principle.

Given:

• Mass of the iron sphere ($m$) = 1 kg
• Initial velocity ($u$) = 20 m/s
• Final velocity ($v$) = 0 m/s (since it comes to rest)
• Distance traveled ($d$) = 50 m

Using the Work-Energy Principle:

The work done by the friction force ($F_{\text{friction}}$) is equal to the change in kinetic energy of the sphere.

1. Initial Kinetic Energy: $\text{Initial Kinetic Energy} = \frac{1}{2} m u^2$ $\text{Initial Kinetic Energy} = \frac{1}{2} \times 1 \times (20)^2 = 200 \, \text{J}$

2. Final Kinetic Energy: $\text{Final Kinetic Energy} = \frac{1}{2} m v^2 = 0 \, \text{J}$

3. Work Done by Friction: $\text{Work Done by Friction} = \text{Change in Kinetic Energy} = \text{Final Kinetic Energy} - \text{Initial Kinetic Energy}$ $\text{Work Done by Friction} = 0 - 200 = -200 \, \text{J}$

4. Relation between Work Done and Force: $\text{Work Done} = F_{\text{friction}} \times d$ $-200 = F_{\text{friction}} \times 50$ $F_{\text{friction}} = \frac{-200}{50} = -4 \, \text{N}$

Result:

The magnitude of the frictional force acting on the sphere is $4 \, \text{N}$ (opposite to the direction of motion).

Would you like any more details, or do you have any questions?

Here are some related questions to expand your understanding:

1. How does the mass of the sphere affect the force of friction?
2. What would be the force of friction if the sphere traveled a different distance?
3. How would the force of friction change if the velocity of the sphere were doubled?
4. Can the force of friction ever be positive in this context?
5. How does the surface on which the sphere travels influence the force of friction?
6. What is the role of kinetic energy in determining the force of friction?
7. How would the problem change if the sphere were not moving on a horizontal surface?
8. What is the importance of the work-energy principle in solving this problem?

Tip: Remember that friction always acts in the direction opposite to the motion of an object, which is why the work done by friction is negative.