A rotten cranberry will lose at least 90% of its total energy during a bounce. If the cranberries are dropped from a height of 10 cm, what is the minimum height in cm of the wall so that no rotten cranberries could ever bounce over it?
ANSWER IS 1CM. SOLUTION TOTAL MECHANICAL ENERGY= TO K.E+P.E =0.5MASS VSQUARE+MASS GH
K.E TOP +P.E TOP= K.E BOTTOM +P.E BOTTOM
0+0.5MVSQUARE=M(9.81)(0.1)
V=1.400 MASS M/SEC
90% LOSE OF ENERGY
M.E=MASS(G)(H) @ THE TOP
M.E=MASS (9.81)(0.1)
M.E=MASS 0.981
REDUCTION OF 90% DURING BOUNCE
M.E= MASS 0.981-MASS 0.981(0.9)
M.E= MASS 0.0981
MASS 0.0981=MASS (9.81)(H)
H=0.01M OR 1CM
edsel salariosa
ANSWER IS 1CM. SOLUTION TOTAL MECHANICAL ENERGY= TO K.E+P.E =0.5MASS VSQUARE+MASS GH
K.E TOP +P.E TOP= K.E BOTTOM +P.E BOTTOM
0+0.5MassVSQUARE=Mass(9.81)(0.1)+0
V=1.400 MASS M/SEC
90% LOSE OF ENERGY
M.E=MASS(G)(H) @ THE TOP
M.E=MASS (9.81)(0.1)
M.E=MASS 0.981
REDUCTION OF 90% DURING BOUNCE
M.E= MASS 0.981-MASS 0.981(0.9)
M.E= MASS 0.0981
MASS 0.0981=MASS (9.81)(H)
H=0.01M OR 1CM
since the mass of a object doesn't given you can cancel both side of the equation and you can find the height
edsel salariosa
research and development engineer
The total energy of the cranberry when it bounces is the same as the initial gravitational potential energy since we can neglect air resistance. Therefore the total energy is mg(10~\mbox{cm})mg(10 cm). After bouncing, the total energy is at most (0.1)mg(10~\mbox{cm})(0.1)mg(10 cm). Therefore the maximum height a rotten cranberry can bounce up is 1~\mbox{cm}1 cm, and if we set our wall at that height no berries can bounce over.
To answer this question, we need to determine the maximum height a rotten cranberry can bounce after losing 90% of its total energy.
First, let's calculate the energy loss. If the cranberry loses 90% of its energy, it retains only 10% of the initial energy after the bounce.
Next, we need to calculate the height the cranberry can reach after bouncing. We can use the principle of conservation of mechanical energy, which states that the initial potential energy (PE_initial) is equal to the final potential energy (PE_final) plus the final kinetic energy (KE_final):
PE_initial = PE_final + KE_final
Since the cranberry starts from rest at the maximum height, the initial kinetic energy (KE_initial) is zero. Therefore:
PE_initial = PE_final
The potential energy is given by the formula:
PE = mgh
Where m is the mass of the cranberry, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
Now, let's assume the mass of the cranberry is negligible compared to its energy loss. The height the cranberry can reach after the bounce is obtained by multiplying the initial height (10 cm or 0.1 m) by the square root of the ratio of the final energy (10%) to the initial energy (100%):
h_final = h_initial * sqrt(E_final / E_initial)
Substituting the values, we get:
h_final = 0.1 m * sqrt(0.1 / 1) = 0.1 m * sqrt(0.1) ≈ 0.0316 m
To ensure no rotten cranberries could ever bounce over the wall, the height of the wall should be greater than this maximum height.
Therefore, the minimum height of the wall would be approximately 0.0316 meters or 3.16 centimeters.