A 6.0kg block is released from rest 80m above the ground. When it has fallen 60m its kinetic energy is:
I got 1200J as my answer
mgh=(6.0*9.81* 60m)=3531.6
PE + KE= (ME + KE)
3531.6 + KE= (6.0*9.81*80m)
KE= 1177.2
is that right
A 6.0 Kg block is thrown up from a point 20m above Earth's surface. At what heights above Earth's surface will the gravitational potential energy of the earth-block system have increase by 500J.
mgh= 2(9.81)(20m)= 392.4 --> potential
500J= mgh
500J = (2kg)(9.81) (h)
h= 25m
someone had told me my actual answer for height should be 45m, because I need to add the 20 I started with.
Thank you
The KE falling sixty meters is 3500J, as you calculated It lost that much gravitational PE, so it is transformed to KE.
If you wnat to do it this way
PE + KE= (ME + KE)
PE(at20) + KE(at20)= (6.0*9.81*80m)
mg20 +KE(at20)= (6.0*9.81*80m)
and solve for KE at 20 , it will be the same as above.
Second question.
mg(distanceup )=500
YOu do not add the 20, because the problem is dealing with INCREASE in PE, not total PE.
So
2(9.81)(h)=500
h= 25m
In the first question, your calculation is correct. The kinetic energy of the block after falling 60m is indeed 1177.2 J.
In the second question, your calculation for the increase in gravitational potential energy is correct. The height above Earth's surface at which the gravitational potential energy of the Earth-block system increases by 500J is 25m.
You do not need to add the initial 20m because the question specifically asks for the increase in gravitational potential energy, not the total. Therefore, the correct answer is indeed 25m.
In the first question, you correctly calculated the potential energy at 60m as 3531.6J and then used the equation PE + KE = ME + KE. However, it seems you made a calculation mistake when solving for KE. The correct value for kinetic energy at 60m is actually 3531.6J - 1177.2J = 2354.4J, not 1177.2J.
In the second question, you correctly calculated the potential energy at 20m as 392.4J. However, when solving for the height above the Earth's surface where the gravitational potential energy increases by 500J, you don't need to add the 20m. The question specifically asks for the height above the Earth's surface, so you only need to consider the change in potential energy from the initial position. Therefore, the correct answer is indeed 25m, not 45m.
It's great that you are showing your calculations and attempting to understand the concepts! Keep practicing and double-checking your work to improve your accuracy.