A stubborn 120-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 (assume the force is horizontal). The
coefficients of friction between the pig and the ground are static = 0.80 and kinetic= 0.50 .Is the farmer able to move the pig?
F = Force required to move pig.
Fp = M*g = 120*9.8 = 1176 N. = Force of pig.
Fs = u*Mg = 0.8*1176 = 941 N. = Force of static friction.
F-Fp-Fs = M*a.
F-1176-941 = 120*0
F = 2117 N.
Well, it sounds like this pig is a real stubborn little porker. Let's see if the farmer has what it takes to move him!
To determine if the farmer can move the pig, we need to compare the force of friction between the pig and the ground to the force applied by the farmer. The force of friction depends on whether the pig is at rest or in motion.
The maximum static friction is given by the equation: Fs = static * Normal force, where the normal force is equal to the weight of the pig since it is on a flat surface. So, Fs = 0.80 * 120 kg * 9.8 m/s² = 941.76 N.
Since the farmer pulls with a force of 800 N, which is less than the maximum static friction of 941.76 N, he won't be able to overcome the static friction and the pig will remain stubbornly in place.
However, if the pig was already in motion, we would need to consider kinetic friction. The force of kinetic friction is given by: Fk = kinetic * Normal force. So, Fk = 0.50 * 120 kg * 9.8 m/s² = 588 N.
In this case, the farmer's force of 800 N is greater than the force of kinetic friction, so once the pig starts moving, the farmer will be able to drag it to the barn. But since the pig has decided to take a stand and not budge, the farmer is out of luck this time!
To determine if the farmer is able to move the pig, we need to compare the force applied by the farmer to the maximum force of static friction between the pig and the ground. If the force applied by the farmer is greater than or equal to the maximum force of static friction, the pig will start moving.
The maximum force of static friction can be calculated using the equation:
static friction force (F_static) = static friction coefficient * normal force
The normal force is equal to the weight of the pig, which can be calculated using the equation:
normal force = mass * gravity
Let's calculate the normal force first:
mass of the pig (m) = 120 kg
acceleration due to gravity (g) = 9.8 m/s^2
normal force = 120 kg * 9.8 m/s^2
normal force = 1176 N
Now, let's calculate the maximum force of static friction:
static friction coefficient (μ_static) = 0.80
F_static = μ_static * normal force
F_static = 0.80 * 1176 N
F_static = 940.8 N
The maximum force of static friction between the pig and the ground is 940.8 N.
Now, let's compare the force applied by the farmer (800 N) to the maximum force of static friction (940.8 N).
Since the force applied by the farmer (800 N) is less than the maximum force of static friction (940.8 N), the pig will not start moving. The farmer is not able to move the pig with his maximum force alone.
To determine if the farmer is able to move the pig, we need to calculate the maximum static frictional force that can be overcome by the farmer's pulling force.
The formula to calculate static friction is: Fs = μs N
Where:
Fs is the static frictional force
μs is the coefficient of static friction
N is the normal force
The normal force (N) is equal to the weight of the pig (W), which can be calculated using the formula: W = m * g
Where:
m is the mass of the pig
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the given values:
m = 120 kg
g = 9.8 m/s^2
W = 120 kg * 9.8 m/s^2
W = 1176 N
Now, we can calculate the maximum static frictional force:
Fs = μs * N
Fs = 0.80 * 1176 N
Fs = 940.8 N
The maximum static frictional force that can be overcome by the farmer's pulling force is 940.8 N.
Since the farmer's maximum pulling force is 800 N, which is less than the maximum static frictional force of 940.8 N, the farmer is not able to move the pig.