A 25 kg cannon ball is fired from a cannon
with muzzle speed of 1520 m/s at an angle of
35.5
◦ with the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
Use conservation of mechanical energy to
find the maximum height reached by first ball.
Answer in units of m.
I AM CONFUSED HOW TO SET UP THE PROBLEM. PLEASE HELP
Vo = 1520m/s[35.5o]
Yo = 1520*sin35.5 = 883 m/s.
KE = 0.5M*Yo^2 = 0.5*25*883^2
KE = 0.5M*Yo^2 = 0.5*25*883^2=9,746,113
J.
PE = KE = Mg*h = 9,746,113
25+9.8*h = 9,746,113
245h = 9,746,113
h = 39,780 m.
To solve this problem using conservation of mechanical energy, you need to consider the initial mechanical energy of the cannonball and its mechanical energy at the maximum height.
The initial mechanical energy of the cannonball includes its kinetic energy (KE) and potential energy (PE) due to its vertical position.
1. Find the initial kinetic energy:
The kinetic energy is given by the equation KE = (1/2)mv^2, where m is the mass of the cannonball (25 kg) and v is the muzzle speed (1520 m/s). Calculate the value of KE at the start.
2. Find the initial potential energy:
The potential energy is given by the equation PE = mgh, where m is the mass of the cannonball (25 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the maximum height (unknown). At the maximum height, the vertical displacement (h) is at a maximum, and thus the potential energy is also at a maximum. Calculate the potential energy at the start.
3. Set up the conservation of mechanical energy equation:
According to the law of conservation of mechanical energy, the sum of the kinetic energy and potential energy at the start should equal the sum of the kinetic energy and potential energy at the maximum height.
KE(start) + PE(start) = KE(max height) + PE(max height)
Substitute the known values for KE(start) and PE(start), and leave the unknown value for PE(max height) as h.
4. Solve for the maximum height (h):
Rearrange the conservation of mechanical energy equation to solve for h, which represents the maximum height reached by the cannonball.
h = (KE(start) + PE(start) - KE(max height))/mg
Substitute the known values for KE(start), PE(start), and mg to find the value of h.
Remember to convert the answer to the required units of meters.
So, the setup involves finding the initial kinetic and potential energy, setting up the conservation of mechanical energy equation, solving for the maximum height.