If a sled reaches the base of the hill with a speed of 15.6m/s, how much work was done by the snow on the sled between points x and y, where x is 3m above the ground with a velocity of 14.30m/s and y is toughing the ground. the sled and the rider are 70kg
Ans: i tried the formula work done = Ek+Ep, where Ek =(0.5)(70)(15.60)^2 and Ep= (70)(9.81)(2) i get 7157j which is incorrect, where am i going wrong?
Hmmm. It has an initial PE, and an initial KE. Then at the bottom it has only KE. So you want to find the work done on friction.
Initial energy-frictionwork=final energy
friction work= initial energy-finalenergy
= 1/2m(14.3^2)+mg*2 - 1/2 m (15.6^2)
Epot=mgh = (70)(9.81)(3)=2060,1
Ek1 =(0.5)(70)(14.30)^2= 7157,15
Ek2 =(0.5)(70)(15.60)^2=8517,6
total energy= (Epot+Ek1)- Ek2
=9217,25-8517,6
=699,65
I object to your use of "total energy". Your formula expression is the same as mine, but I found the work done on friction. That is not, nor even close to, total energy. So I am not certain what you mean. You found friction work. I also object to the number of significant digits, carrying these calculations to 5 or 6 places is lubricious. You also should use units, the final answer is in Joules (J). I did not check your calculator work.
i agree with you but is the result correct, my english is'nt ok i know
i forgot the units, but sure it is joule
To calculate the work done, you need to consider the changes in kinetic energy (Ek) and gravitational potential energy (Ep). It seems like you have correctly identified the formulas for Ek and Ep.
The change in kinetic energy (ΔEk) can be calculated using the formula ΔEk = 0.5 * m * (vf^2 - vi^2), where m is the mass of the sled and rider, vf is the final velocity, and vi is the initial velocity.
In this case, the mass (m) is given as 70 kg, the final velocity (vf) is given as 15.6 m/s, and the initial velocity (vi) is given as 14.30 m/s.
ΔEk = 0.5 * 70 * (15.6^2 - 14.30^2)
= 0.5 * 70 * (243.36 - 204.49)
= 0.5 * 70 * 38.87
= 0.5 * 2710.9
= 1355.45 J
The change in gravitational potential energy (ΔEp) can be calculated using the formula ΔEp = m * g * (hf - hi), where g is the acceleration due to gravity (9.81 m/s^2), hf is the final height above the ground, and hi is the initial height above the ground.
In this case, the mass (m) is given as 70 kg, the initial height (hi) is given as 3 m, and the final height (hf) is 0 m (touching the ground).
ΔEp = 70 * 9.81 * (0 - 3)
= 70 * 9.81 * -3
= -2061.03 J
Note that the negative sign indicates a decrease in gravitational potential energy as the sled moves downhill.
Now, to calculate the total work done (W), you should sum up the changes in kinetic energy and gravitational potential energy:
W = ΔEk + ΔEp
= 1355.45 + (-2061.03)
= -705.58 J
The resulting work done by the snow on the sled is -705.58 J, indicating that work is being done on the sled by the snow.