A force of 7000N is applied to drag a 500 kg cow across a flat level floor to McSlaughter House. The cow has an acceleration of 2.5 m/s2.
(a) what's the weight of the cow?
(b) what is the normal force acting on the cow?
(c) What is the resultant force that causes the cow to accelerate?
(d) Is the friction acting on the cow Static or Kinetic?
(e) What is the coefficient of friction?
(a) w = m g
(b) equal to weight
(c) f = m a = 500 * 2.5
(d) moving (kinetic)
(e) k = (7000 - 1250) / (m g)
To solve these questions, we will use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. We will also consider the concepts of weight, normal force, and friction.
(a) To calculate the weight of the cow, we use the equation:
Weight = mass × acceleration due to gravity
Given that the mass of the cow is 500 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:
Weight = 500 kg × 9.8 m/s² = 4900 N
Therefore, the weight of the cow is 4900 N.
(b) The normal force acting on an object is equal in magnitude and opposite in direction to the weight of the object. In this case, since the cow is on a flat level floor, the normal force will be equal to its weight. Therefore, the normal force acting on the cow is also 4900 N.
(c) The resultant force that causes the cow to accelerate is the net force acting on it. We can calculate this force using Newton's second law:
Force = mass × acceleration
Given that the mass of the cow is 500 kg and the acceleration is 2.5 m/s², we can calculate the resultant force:
Force = 500 kg × 2.5 m/s² = 1250 N
Therefore, the resultant force that causes the cow to accelerate is 1250 N.
(d) To determine if the friction acting on the cow is static or kinetic, we need to compare it with the maximum static friction that can be exerted. If the applied force exceeds the maximum static friction, the friction becomes kinetic.
Since the force applied (7000 N) is greater than the maximum static friction, we can conclude that the friction acting on the cow is kinetic.
(e) The coefficient of friction is a value that represents the interaction between two surfaces in contact. In this case, we can calculate the coefficient of kinetic friction using the formula:
Coefficient of friction (kinetic) = Force of friction / Normal force
Given that the force of friction is equal to the applied force (7000 N) and the normal force is 4900 N, we can calculate the coefficient of friction:
Coefficient of friction (kinetic) = 7000 N / 4900 N = 1.43
Therefore, the coefficient of friction in this case is 1.43.
To answer these questions, we need to understand a few concepts related to forces and motion. The information given in the question is sufficient to calculate the answers, but I'll explain the relevant equations and steps along the way.
(a) The weight of an object can be calculated using the formula:
Weight (W) = mass (m) * acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s². In this case, the mass of the cow is given as 500 kg. So, we can calculate the weight of the cow:
Weight (W) = 500 kg * 9.8 m/s² = 4900 N
Therefore, the weight of the cow is 4900 N.
(b) The normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. In this case, since the cow is on a flat level floor, the normal force would be equal in magnitude and opposite in direction to the weight of the cow.
Normal force = Weight of the cow = 4900 N
So, the normal force acting on the cow is 4900 N.
(c) The resultant force is the net force acting on the cow that causes it to accelerate. It can be calculated using Newton's second law of motion:
Resultant force (F) = mass (m) * acceleration (a)
In this case, the mass of the cow is given as 500 kg and the acceleration is given as 2.5 m/s². So, we can calculate the resultant force:
Resultant force (F) = 500 kg * 2.5 m/s² = 1250 N
Therefore, the resultant force that causes the cow to accelerate is 1250 N.
(d) To determine if the friction acting on the cow is static or kinetic, we need to compare the applied force (7000 N) and the maximum frictional force (which occurs when the cow is not moving).
If the applied force is greater than the maximum static frictional force, the cow will start moving and the friction acting on it will be kinetic. However, if the applied force is less than or equal to the maximum static frictional force, the cow will remain at rest or move at a constant velocity, and the friction acting on it will be static.
In this case, if the resultant force (1250 N) is less than the maximum static frictional force, then the friction acting on the cow will be static. Otherwise, it will be kinetic.
(e) The coefficient of friction (μ) can be determined using the equation:
Frictional force (Ff) = coefficient of friction (μ) * Normal force
In this case, the normal force is 4900 N (the weight of the cow) and the frictional force can be calculated using the resultant force and weight of the cow:
Frictional force (Ff) = Resultant force - Weight of the cow
If the friction is static, then the frictional force will be equal to the applied force (7000 N). We can use this equation to calculate the coefficient of friction:
7000 N = μ * 4900 N
Solving for μ:
Coefficient of friction (μ) = 7000 N / 4900 N = 1.43
Therefore, the coefficient of friction is 1.43.
To summarize:
(a) The weight of the cow is 4900 N.
(b) The normal force acting on the cow is 4900 N.
(c) The resultant force that causes the cow to accelerate is 1250 N.
(d) The friction acting on the cow is static if the resultant force (1250 N) is less than the maximum static frictional force; otherwise, it is kinetic.
(e) The coefficient of friction is 1.43.