To solve this problem, we'll first determine the maximum static friction force that can act on the crate. The static friction force is what prevents the crate from moving until a certain maximum force is exceeded. The formula for the maximum static friction force $f_s$ is:

$f_s = \mu_s \cdot F_n$

where:

• $\mu_s$ is the coefficient of static friction (0.5 in this case),
• $F_n$ is the normal force acting on the crate.

The normal force $F_n$ is equal to the gravitational force acting on the crate (since it’s on a flat surface). The gravitational force is given by:

$F_n = m \cdot g$

where:

• $m$ is the mass of the crate (122 kg),
• $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$).

Step 1: Calculate the normal force

$F_n = 122 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 1195.6 \, \text{N}$

Step 2: Calculate the maximum static friction force

$f_s = 0.5 \cdot 1195.6 \, \text{N} = 597.8 \, \text{N}$

So, the maximum force you can exert horizontally on the crate without moving it is 597.8 N.

Let me know if you'd like further details or have any questions.

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Here are 5 related questions:

1. What happens if the applied force exceeds the maximum static friction?
2. How does the coefficient of kinetic friction affect the motion once the crate starts moving?
3. What is the force of kinetic friction on the crate once it is in motion?
4. How does the mass of the crate affect the maximum static friction?
5. How would the situation change if the crate was on an inclined plane?

Tip: Static friction is always greater than or equal to kinetic friction for most materials.