Question involving Newton's Laws and Friction

In summary, a worker pulling with a force of 45N on a rope attached to a 10 kg crate on a rough floor will experience a frictional force of 45N, equal to the pulling force. This is because the normal force is equal to the weight of the crate, and the frictional force is calculated using the coefficient of friction and the normal force. In this case, the force of pull is equal to the frictional force.
  • #1
Chandasouk
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Homework Statement



A worker pulls horizontally on a rope that is attached to a 10 kg crate that is resting on a rough floor. The coefficients of static and kinetic friction are 0.5 and 0.3 respectively. The worker pulls with a force of 45N. What is the frictional force exerted by the surface?

We did this in class and the answer was 45N but I do not understand why that is. Can someone explain?
 
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  • #2
A worker pulls horizontally on a rope that is attached to a 10 kg crate that is resting on a rough floor. The coefficients of static and kinetic friction are 0.5 and 0.3 respectively. The worker pulls with a force of 45N. What is the frictional force exerted by the surface?

We did this in class and the answer was 45N but I do not understand why that is. Can someone explain?

So vertical direction of the pull does not need to be taken into account, therefore the normal force = weight.

The weight = mg or (10kg)(9.8) = 98 N

so the normal force = 98N

since f = (coefficient) * N

f = .5 * 98 = 49N, so the worker would need to pull with a force GREATER than 49 N in order to start accelerating the box, but since he pulls with only 45N, the force of friction will be equal to the pulling force..

so therefore f = force of pull = 45 N

so f = 45N
 
  • #3


I can provide an explanation for why the frictional force is equal to the applied force of 45N in this scenario. According to Newton's Second Law, the net force on an object is equal to its mass multiplied by its acceleration. In this case, the crate has a mass of 10 kg and is at rest, so its acceleration is 0 m/s^2. Therefore, the net force acting on the crate must also be 0N in order for it to remain at rest.

However, the worker is exerting a horizontal force of 45N on the crate. This means that there must be an equal and opposite force acting on the crate in the opposite direction, in order to satisfy Newton's Third Law. This force is the frictional force exerted by the rough floor on the crate.

The coefficient of static friction, 0.5, tells us that the maximum frictional force that can be exerted by the surface is 0.5 times the normal force. In this case, the normal force is equal to the weight of the crate, which is 10 kg multiplied by the acceleration due to gravity, 9.8 m/s^2, giving us a normal force of 98N.

Since the applied force of 45N is less than the maximum frictional force of 0.5 x 98N = 49N, the crate remains at rest and the frictional force is equal to the applied force of 45N. This is why the answer is 45N.

If the applied force was greater than 49N, the crate would start to move and the coefficient of kinetic friction, 0.3, would come into play. This coefficient tells us that the kinetic frictional force is 0.3 times the normal force. So, if the crate was moving, the frictional force would be 0.3 x 98N = 29.4N, which is less than the applied force of 45N. This would result in the crate accelerating in the direction of the applied force.

I hope this explanation helps you understand why the frictional force is equal to the applied force in this scenario. It is important to remember that frictional forces can vary depending on the situation and the coefficients involved, but they will always act in the opposite direction of the applied force.
 

FAQ: Question involving Newton's Laws and Friction

What are Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental laws that describe the motion of objects in the presence of external forces. The first law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

How do Newton's Laws relate to everyday life?

Newton's Laws of Motion can be observed in many everyday situations. For example, the first law can be seen when a person in a moving car suddenly stops and their body continues to move forward due to inertia. The second law can be seen when pushing a shopping cart - the harder you push, the faster it accelerates. The third law can be seen in activities like walking or swimming, where the action of pushing against the ground or water creates an equal and opposite reaction that propels the person forward.

What is friction and how does it affect motion?

Friction is the force that opposes motion between two surfaces in contact. It is caused by the roughness of the surfaces and the interlocking of their microscopic irregularities. Friction can either slow down or prevent motion, making it an important factor in everyday life and in understanding the motion of objects. For example, friction between the tires of a car and the road is necessary for the car to move, but too much friction can cause the car to skid or lose control.

How does the coefficient of friction affect the amount of friction?

The coefficient of friction is a measure of the roughness of two surfaces in contact. It is a dimensionless value that ranges from 0 (no friction) to 1 (maximum friction). The higher the coefficient of friction, the more force is required to overcome the friction and move an object. For example, a rough surface like sandpaper will have a higher coefficient of friction than a smooth surface like ice, meaning it will require more force to move an object across it.

How can friction be reduced?

There are several ways to reduce friction, including using lubricants, making surfaces smoother, and reducing the weight of an object. Lubricants like oil or grease create a thin layer between two surfaces, reducing the amount of direct contact and therefore reducing friction. Smoothing surfaces can also reduce friction by eliminating or reducing the interlocking of microscopic irregularities. Finally, reducing weight can also reduce friction, as there is less force pushing down on the surfaces in contact.

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