Mechanical Energy vs Potential Energy & Kinetic Energy

In summary, the conversation discussed calculating the minimum speed needed for a hammer to hit a wooden block and cause a metal bar to ring a bell 9.0 m above. The calculation involved using the mass, height, and gravitational acceleration to determine the potential energy, which was then used to calculate the kinetic energy required for the hammer. The final answer was determined to be 5.9 m/s, which is a more reasonable velocity compared to the initial calculation of 104 m/s.
  • #1
Lexington
4
0
[SOLVED] Mechanical Energy vs Potential Energy & Kinetic Energy

I'm pretty sure I did this one wrong, =( please help clarify?

8. At the Calgary Stampede, you can win a prize if the bell rings when you strike a wooden block with a 10.0-kg hammer. The block is at one end of a lever. The other end of the lever drives a 2.0-kg metal bar up a slide to ring the bell 9.0 m above. What is the minimum speed the hammer must be swung to make the bar hit the bell?

Assuming there are no energy losses, the energy required to be transmitted to the 2.0-kg bar can be calculated and used as the kinetic energy required for the hammer.



Ek = 1/2mv^2
Ep = mgh
Em = Ep + Ek
v = √[(2•Ek)/m]




m1 = 10.0kg
m2 = 2.0kg
mt = m2 + m1 = 12.0kg
D = 9.0m

Ep = mgh
= (2.0kg)(9.0m)(9.81m/s^2)
= 176.58 J

Hammer:
h = 0m
v = √[(2•Ek)/m] + mgh
= √[(2•176.58J)/10.0kg] + (10.0kg)(9.81m/s^2)
= 104.042726646919
v = 1.0x10^2 m/s

The hammer should have a velocity of 1.0x10^2 J when it hits the wooden block, causing 1.77x10^2 J of energy on the 2.0kg block.
 
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  • #2
Lexington said:
Hammer:
h = 0m
v = √[(2•Ek)/m] + mgh
= √[(2•176.58J)/10.0kg] + (10.0kg)(9.81m/s^2)*0
:wink:
 
  • #3
Thank you! 5.9 m/s sounds allot better than 104m/s haha!
 
  • #4
Lexington said:
Thank you! 5.9 m/s sounds allot better than 104m/s haha!
A pleasure :smile:
 

What is mechanical energy?

Mechanical energy is the energy that is possessed by an object due to its motion or position. It is the sum of potential energy and kinetic energy.

What is the difference between potential energy and kinetic energy?

Potential energy is the energy that an object has due to its position or condition, such as the energy stored in a stretched spring or a raised object. Kinetic energy, on the other hand, is the energy that an object possesses due to its motion. It is dependent on an object's mass and velocity.

Can potential energy be converted into kinetic energy?

Yes, potential energy can be converted into kinetic energy and vice versa. When an object's position changes, its potential energy changes, and when the object starts moving, its potential energy is converted into kinetic energy.

What are some examples of mechanical energy?

Some examples of mechanical energy include a moving car, a spinning top, a falling object, a swinging pendulum, and a stretched rubber band.

How is mechanical energy important in everyday life?

Mechanical energy is important in everyday life because it powers many of the devices and machines that we use, such as cars, bicycles, and appliances. It also plays a crucial role in many natural phenomena, such as the movement of wind and water, and the functioning of our bodies.

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