Conservation of Energy: Finding the Speed of a Falling Ball

In summary, the coefficient of friction between a block of mass 3.00kg and a surface is 0.400. The system starts from rest and the question is asking for the speed of a ball of mass 5.00kg after falling a distance of 1.50m. To solve this problem, the equation Ui + Ki + ΔEmech = Uf + Kf is used, with the gravitational potential energy and kinetic energy of the ball and block being taken into account. However, care must be taken to correctly determine the direction of these energies, as sign errors can result in an incorrect answer.
  • #1
sireh
2
0

Homework Statement


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The coefficient of friction between the block of mass m1 = 3.00kg and the surface in Figure P7.22 is μk = 0.400. The system starts from rest. What is the speed of the ball of mass m2 = 5.00 kg when it has fallen a distance of h = 1.50m?

Homework Equations


This is in the chapter on conservation of energy, so
Ui + Ki + ΔEmech = Uf + Kf

The Attempt at a Solution


Using downward direction as positive so g is positive

m2gh - fh = 1/2(m1 + m2)v2
(5.00kg)(9.8m/s2)(1.5m) - (-11.76N)(1.5m) = 1/2(3.00kg + 5.00kg)v2
91.14Nm = 4kg * v2
22.785Nm2/s2 = v2
4.77m/s = v

That's not the answer that I'm seeing on the answer sheet. I'm not sure what I did wrong.
 
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  • #2
sireh said:
m2gh - fh = 1/2(m1 + m2)v2
(5.00kg)(9.8m/s2)(1.5m) - (-11.76N)(1.5m) = 1/2(3.00kg + 5.00kg)v2
Think conceptually and decide if you want to have two minus signs here.
 

FAQ: Conservation of Energy: Finding the Speed of a Falling Ball

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but it can only be transformed from one form to another.

Why is conservation of energy important?

Conservation of energy is important because it helps us understand how energy is transferred and used in different systems. It also allows us to make more sustainable and efficient use of energy resources.

What are some examples of conservation of energy in action?

Some examples of conservation of energy include a pendulum swinging back and forth, a ball rolling down a hill, and a battery powering a lightbulb. In each of these examples, energy is transferred from one form to another, but the total amount of energy remains constant.

What happens when energy is not conserved?

When energy is not conserved, it can lead to wastage or inefficiency in energy usage. This can result in higher energy costs and negatively impact the environment.

How can we practice conservation of energy in our daily lives?

We can practice conservation of energy by using energy-efficient appliances, turning off lights and electronics when not in use, using public transportation or carpooling, and being mindful of our energy consumption habits. Small actions can make a big impact in conserving energy and protecting our planet.

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