Velocity, Force of Friction, and Total Energy in a System Question

In summary, the problem involves a 200 kg boulder falling from a 120.0 m high cliff with a frictional force of 280 N[U]. The goal is to find the velocity of the boulder just before it hits the ground. Using the equations for kinetic energy, gravitational potential energy, and work, the total force is calculated to be 235200 J and the work done by friction is 33600 J. Subtracting the work done by friction from the total energy, the kinetic energy is found to be 201600 J. However, the answer may be incorrect due to the assumption of a constant frictional force.
  • #1
Killic
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Homework Statement


A 200 kg boulder falls from rest off a 120.0 m high cliff. If the boulder experiences a frictional force of 280 N as it falls, what would be the velocity just before it hits the ground?

Homework Equations



kinetic energy = (1/2)mv2
gravitational potential energy = mgh
work = (net force)(Δd)

The Attempt at a Solution


Total force = mgh = 200kg*9.8N/kg*120m = 235200 J

Wfriction = FΔd
Wfriction = 280 N*120 m
Wfriction = 33600 J

total energy = kinetic energy + work done by friction
kinetic energy = 235200 J - 33600 J
kinetic energy = 201600 J
201600 J = (1/2)mv2
v = 45 m/s

However, according to my teacher, this answer is incorrect.
 
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  • #2
What does your notation "N" represent? If, as I suspect, it is saying that the friction force is proportional to velocity (this is typical for air drag), then your treatment of the friction as constant is not appropriate here.
 

What is velocity and how is it related to force of friction?

Velocity is a measure of the rate of change of an object's position over time. It is often described as the speed of an object in a particular direction. Force of friction is the force that opposes the motion of an object as it moves over a surface. The force of friction is directly related to an object's velocity, as an increase in velocity will result in an increase in the force of friction.

How does force of friction affect the total energy in a system?

The force of friction acts in the opposite direction of an object's motion, causing it to slow down and eventually come to a stop. This decrease in velocity results in a decrease in kinetic energy, which is a form of energy associated with an object's motion. Therefore, force of friction ultimately decreases the total energy in a system.

What factors affect the force of friction?

The force of friction is affected by several factors, including the type of surface the object is moving over, the weight of the object, and the roughness of the surface. Generally, rougher surfaces and heavier objects will result in a greater force of friction.

How is the total energy in a system conserved?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In a system, the total energy remains constant, meaning that the total amount of energy before and after an event will be the same. This includes the energy of objects in motion, such as kinetic energy, and the potential energy of objects due to their position or shape.

What is the difference between kinetic and potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or shape. Kinetic energy is directly related to an object's velocity, while potential energy is related to an object's height or distance from the ground. Both forms of energy are important in understanding the total energy in a system.

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