A 2kg. lump of clay traveling at a speed of 20m/s collides with and sticks to a 5kg. lump of clay initially at rest and hanging from a string. Find the final speed of the new lump of clay. How high will the clay swing after the collision?
(initial)
m1=2kg.
v1=20m/s
(final)
m2=2+5=7kg.
v2=?
KEi=PEf
(1/2)(2kg.)(20m/s)^2=(7kg.)(9.81m/s^2)(h)
solve for h=?
h=5.825m
solve for v2=?
v2=(2gh)^1/2
v2=10.69m/s
My friend was very adamant in telling me that the h=1.66m. Either I messed up in the equation I used or he did.
You are very wrong.
first, v2: conservation of momentum applies 2*20=(2+5)V or V= 2/7 *20 m/s
Now, the KE this has is 1/2 m v^2 or
1/2 (7)(4/49 * 400) work that out.
this is now equal to mgh or 7*9.81*h
solve for h.
To find the final speed of the new lump of clay, we can use the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum of the system.
Initial momentum: m1 * v1
Final momentum: m2 * v2
m1 = 2 kg (mass of the first lump of clay)
v1 = 20 m/s (speed of the first lump of clay)
m2 = 7 kg (combined mass of both lumps of clay after collision)
v2 = Final speed of the new lump of clay (what we want to find)
Using the principle of conservation of momentum:
m1 * v1 = m2 * v2
(2 kg) * (20 m/s) = (7 kg) * v2
40 kg m/s = 7 kg * v2
v2 = 40 kg m/s / 7 kg
v2 ≈ 5.71 m/s
Therefore, the final speed of the new lump of clay is approximately 5.71 m/s.
To find the height the clay swings after the collision, we can use the principle of conservation of energy. The initial kinetic energy of the system is equal to the final potential energy of the system.
Initial Kinetic Energy: (1/2) * m1 * (v1)^2
Final Potential Energy: m2 * g * h
m1 = 2 kg (mass of the first lump of clay)
v1 = 20 m/s (speed of the first lump of clay)
m2 = 7 kg (combined mass of both lumps of clay after collision)
g = 9.81 m/s^2 (acceleration due to gravity)
h = height we want to find
Using the principle of conservation of energy:
(1/2) * (2 kg) * (20 m/s)^2 = (7 kg) * (9.81 m/s^2) * h
200 J = 68.67 kg m^2/s^2 * h
h = 200 J / (68.67 kg m^2/s^2)
h ≈ 2.91 m
Therefore, the height the clay swings after the collision is approximately 2.91 m.
Based on the calculations, it seems that your friend's value of h=1.66 m is incorrect.