Verify Answers to Mechanical Energy Homework

In summary, by pulling a child back on a swing, whose chain is 2.0 m long, until the swing makes an angle of 30.0° with the vertical, you do 100 J of work and the child's mass is 38.21 kg. Upon releasing the swing from this position, the child will have a speed of 2.287 m/s at the bottom of the arc.
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goonking
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Homework Statement


You do 100 J of work while pulling a child back on a swing, whose chain is 2.0 m long, until the swing makes an angle of 30.0° with the vertical. a) What is the child's mass? (Consider the swing itself and the chain massless) b) Upon releasing the swing from this position, what will the speed of the child be at the bottom of the arc?

Homework Equations


mgh = 1/2 mv^2

The Attempt at a Solution


After doing some trig, I get the height difference of the swing to be 0.267m; we now have h in mgh.

since he exerted 100 Js, we set mgh = 100, solving for m

m = 38.21 kg

now we want to find the speed at the bottom of the arc.

we set mgh = 1/2 mv^2

Mass cancels out

we solve for V, which should be 2.287 m/s.

Can someone verify if my answers are correct?
 
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  • #2
Your work looks good to me.
 
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Related to Verify Answers to Mechanical Energy Homework

1. What is mechanical energy?

Mechanical energy is defined as the sum of potential energy and kinetic energy in a system. Potential energy is the energy stored in an object due to its position or configuration, while kinetic energy is the energy an object possesses due to its motion.

2. How is mechanical energy conserved?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In a closed system, mechanical energy is conserved because potential energy can be converted into kinetic energy and vice versa.

3. What are some examples of mechanical energy?

Some examples of mechanical energy include a swinging pendulum, a moving car, a bouncing ball, and a spinning top. In each of these examples, there is a transfer of energy between potential and kinetic forms.

4. How is mechanical energy different from other forms of energy?

Mechanical energy is a type of kinetic energy that specifically relates to the motion or position of an object. Other forms of energy include potential energy, thermal energy, chemical energy, and electromagnetic energy.

5. How is mechanical energy measured?

Mechanical energy is measured in joules (J). The formula for calculating mechanical energy is ME = PE + KE, where ME is mechanical energy, PE is potential energy, and KE is kinetic energy. Both potential and kinetic energy are measured in joules as well.

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