49 J is the total kinetic energy. If a bowling ball of mass 7.3 kg and radius 9.6 cm rolls without slipping down a lane at 3.1 m/s. Kinetic energy is the energy an bowling ball has because of its motion.
Given: m = 7.3 Kg ; r = 9.4 cm = 0.094 m ; v = 3.1 m
Now total kinetic energy in this case is given by KE = Kinetic energy due to rotation + Kinetic energy due to translation
i,e KE = 1/2*m*v2 + 1/2*I*ω2 where I is the moment of inertia of the bowling ball about it's center and ω is the angular velocity
Now for pure rotation (without slipping) v = rω
also for the ball (solid sphere) I = 2/5*m*r2
Hence our kinetic energy becomes
KE = 1/2*m*v2 + 1/5*m*v2 = 7/10*m*v2
so KE = 0.7*7.3*(3.1)2 = 49.10 J = 49 J
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Earth's land and ocean surface to the atmosphere.
Answer:
The speed of the raft is 1.05 m/s
Explanation:
The equation for the position of the stone is as follows:
y = y0 + v0 · t + 1/2 · g · t²
Where:
y = height of the stone at time t
y0 = initial height
v0 = initial speed
t = time
g = acceleration due to gravity
The equation for the position of the raft is as follows:
x = x0 + v · t
Where:
x = position of the raft at time t
x0 = initial position
v = velocity
t = time
To find the speed of the raft, we have to know how much time the raft traveled until the stone reached the river. For that, we can calculate the time of free fall of the stone:
y = y0 + v0 · t + 1/2 · g · t² (v0=0 because the stone is dropped from rest)
If we place the origin of the frame of reference at the river below the bridge:
0 m = 95.6 m - 9.8 m/s² · t²
-95.6 m / -9,8 m/s² = t²
t = 3.12 s
We know that the raft traveled (4.84 m - 1.56 m) 3.28 m in that time, then the velocity of the raft will be:
x/t = v
3.28 m / 3.12 s = v
v = 1.05 m/s
A ) 14 billion years = 14,000,000,000
b ) 1 year = 365 · 24 · 3,600 = 31,536 · 10³
