Let's solve the problem based on the information provided in the image.

Problem Summary:

• Mass of the crate $m = 8 \, \text{kg}$
• Gravitational force $F_{\text{grav}} = 80 \, \text{N}$ (this implies gravity $g = 10 \, \text{m/s}^2$)
• Applied force $F_{\text{app}} = 50 \, \text{N}$
• Frictional force $F_{\text{frict}} = 10 \, \text{N}$

We need to find the acceleration of the crate.

Step-by-step solution:

1. Net Force Calculation: The net force acting on the crate in the horizontal direction is the difference between the applied force and the frictional force: $F_{\text{net}} = F_{\text{app}} - F_{\text{frict}}$ Substituting the values: $F_{\text{net}} = 50 \, \text{N} - 10 \, \text{N} = 40 \, \text{N}$

2. Applying Newton's Second Law: According to Newton's second law, the net force is equal to mass times acceleration: $F_{\text{net}} = m \cdot a$ Solving for acceleration $a$: $a = \frac{F_{\text{net}}}{m} = \frac{40 \, \text{N}}{8 \, \text{kg}} = 5 \, \text{m/s}^2$

Final Answer:

The acceleration of the crate is 5 m/s².

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

Here are 5 related questions to expand on this topic:

1. How would the acceleration change if the applied force were increased to 60 N?
2. What happens to the acceleration if the frictional force is doubled to 20 N?
3. How would the result differ if the surface were frictionless?
4. How can you calculate the normal force acting on the crate?
5. What role does the gravitational force play in this scenario?

Tip: Newton's second law is essential for understanding how forces result in motion and how acceleration is determined.