# A stubborn 110 kg pig sits down and refuses to move. To drag the pig to the barn, the exasperated farmer ties a rope around the pig and pulls with his maximum force of 800 N. The coefficients of friction between the pig and the ground are μs=0.80 and μk=0.50.

Calculate the force which farmer needs to apply to budge the pig.

## Well, it seems like the stubborn pig is enjoying a little game of "tug-of-war" with the farmer. Let's calculate the force needed to budge our hefty friend.

First, we need to determine the maximum force of static friction (Ff_max) that opposes the farmer's pulling force. We can calculate this using the equation:

Ff_max = coefficient of static friction * normal force

The normal force (Fn) can be calculated using the equation:

Fn = mass * gravitational force

The gravitational force (Fg) can be calculated using:

Fg = mass * acceleration due to gravity

Since the pig's mass is 110 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we have:

Fg = 110 kg * 9.8 m/s^2 = 1078 N

Now, let's calculate the maximum force of static friction:

Ff_max = 0.80 * 1078 N = 862.4 N

Since the farmer is exerting his maximum force of 800 N, it's still less than the force of static friction. Therefore, the pig remains stubbornly seated.

But let's just imagine the farmer decides to channel his inner superhero and applies an even greater force than the maximum static friction force. In that case, the equation for kinetic friction comes into play.

The force of kinetic friction (Fk) can be calculated using:

Fk = coefficient of kinetic friction * normal force

In this case, the normal force remains the same. So, let's calculate the force of kinetic friction:

Fk = 0.50 * 1078 N = 539 N

So, the farmer would need to exert a force of at least 539 N to budge the pig once it starts moving.

However, it's worth mentioning that this calculation assumes ideal conditions, and in reality, various factors could affect the force required, such as uneven ground or the pig's willingness to cooperate. Just remember, when in doubt, ask the pig if it wants to dance!

## To calculate the force required to budge the pig, we need to consider the maximum static friction force. The maximum static friction force, F_s, can be calculated using the formula:

F_s = μs * N

Where μs is the coefficient of static friction and N is the normal force.

Given that the weight of the pig is 110 kg, the normal force N acting on it can be calculated as:

N = m * g

Where m is the mass of the pig and g is the acceleration due to gravity.

Given:
m = 110 kg
g = 9.8 m/s^2

N = 110 kg * 9.8 m/s^2 = 1078 N

Now we can calculate the maximum static friction force:

F_s = μs * N
= 0.80 * 1078 N
= 862.4 N

Since the farmer is pulling with his maximum force of 800 N, which is less than the maximum static friction force, the pig will not budge.

Therefore, the force required to budge the pig is equal to the maximum static friction force, which is 862.4 N.

## To calculate the force needed to budge the pig, we need to consider the static and kinetic friction between the pig and the ground.

Static friction is the force that opposes the initial motion of two surfaces in contact when they are at rest relative to each other. Once the pig starts moving, the force of static friction is overcome by the applied force. The force of static friction can be calculated using the equation:

fs = μs * N

where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force between the pig and the ground.

The normal force acting on an object is equal to the weight of the object, which can be calculated as:

N = m * g

where m is the mass of the pig (110 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Now we can calculate the force of static friction:

fs = μs * N
= μs * m * g

Next, we need to compare the force of static friction to the maximum force applied by the farmer (800 N). If the maximum force applied by the farmer is less than or equal to the force of static friction, the pig will not budge.

In this case, let's assume that the force of static friction is greater than the maximum force applied by the farmer. Therefore, the pig remains stationary. However, if the applied force was greater than or equal to the force of static friction, the pig would start to move.

Once the pig starts moving, the force of kinetic friction comes into play. The force of kinetic friction is given by:

fk = μk * N
= μk * m * g

In this case, we can calculate the force of kinetic friction:

fk = μk * N
= μk * m * g

Finally, to calculate the force needed to budge the pig, we need to find the force required to overcome the force of static friction.

Force required = force of static friction + force of kinetic friction

Force required = fs + fk

Substituting the given values into the equations:

fs = μs * m * g
fk = μk * m * g

Finally, calculate the force required.