YOU THROW A 1.00 KG STONE HORIZONTALLY OFF THE EDGE OF A 10.0 M HIGH CLIFF WITH
ID: 2182994 • Letter: Y
Question
YOU THROW A 1.00 KG STONE HORIZONTALLY OFF THE EDGE OF A 10.0 M HIGH CLIFF WITH AN INITIAL VELOCITY OF 8.00 M/S.
HOW FAST IS THE BALL GOING? (NEGLECT THE EFFECTS OF AIR RESISTANCE)
1.Use energy ideas to find Vf. Energy conservative tells you that whatever initial energy you start with, you'll have that amount at the end: Ef=Ei. Do this part without plugging in numbers until the end. Just work with variables.
A: in this problem, the ball only has kinetic and gravitational potential energy. Write down the expression that gives you Ui, Ki, Ei: Ei=Ui+Ki=________
B: Do the same for the ball at the bottom of the cliff: Ef=Uf+Kf=________
C: now using the fact that you know Ef=Ei, put your expressions for the initial and final energy together and solve for Vf.
D: do you get the same value for Vf when using kinematics? explain why or why not?
E: Explain whether kinematic or energy is more difficult?
F: did you need to know that the mass of the stone was 1-kg to find Vf? explain.
G: Is there any quantity that you can calculate using the kinematics approach that you cant find using only the energy approach?
Explanation / Answer
1) vf=?
horizontal velocity= 8 m/sec
vertical velocity at the end (v)=sqrt(2gh)
v=sqrt(2*9.8*10)= 14 m/sec
vf=sqrt(8^2+14^2)
vf= 16.1245 m/sec
A) at the top
potential energy Ui= mgh= 1*9.8*10= 98 J
initial kinetiic energy Ki= 0.5*1*8^2= 32 J
total Ei=98+32= 130 J
B) at the bottom
potential energy Uf=0
kinetic energy be Kf
C) Ei=Ef=Kf+Pf
130=0.5*1*vf^2
vf= sqrt(260)
vf=16.1245 m/sec
D) as there is no loss of energy in the motion and also the motion is uniform so the value of vf is same in both the cases
E) calculating using kinematics is more difficult compared to energy conservation. the energy case does not depend on the type of motion and also the position of the object. here we equate the initial and the final energy. where as for kinematics any change in the motion may complicat ethe study of motion which makes it difficult to calculate
F) we need not know the mass of the body to calculate the fiinal velocity. in kinematic way of solving the problem, the mass is not a parameter in the calculation process. as the motion of the body is uniform and there is no resistance, the change in mass of the body doesnot affect the final velocity.
G) we cancalculate the distance from the cliff where the body meets the ground. whereas using the energy conservation method we cant find this distance.
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