Answer:
d) 700 m/s
Explanation:
if k is the force constant and x is the maximum compression distance, then:
the potential energy the spring can acquire is given by:
U = 1/2×k×(x^2)
and, the kinetic energy system is given by:
K = 1/2×m×(v^2)
if Ki is the initial kinetic energy of the system, Ui is the initial kinetic energy of the system and Kf and Uf are final kinetic and potential energy respectively then, According to energy conservation:
initial energy = final energy
Ki +Ui = Kf +Uf
Ui = 0 J and Kf = 0J
Ki = Uf
1/2×m×(v^2) = 1/2×k×(x^2)
m×(v^2) = k×(x^2)
v^2 = k×(x^2)/m
= (500)×((21×10^-2)^2)/(19×10^-3 + 8)
= 2.75
v = 1.66 m/s
the v is the final velocity of the bullet block system, if m1 is the mass of bullet and M is the mass of the block and v1 is the initial velocity of the bullet while V is the initial velocity of the block, then by conservation linear momentum:
m1×v1 + M×V = v×(m1 + M) but V = 0 because the block is stationary, initially.
m1×v1 = v×(m1 + M)
v1 = v×(m + M)/(m1)
= (1.66)×(19×10^-3 + 8)/(19×10^-3)
= 699.86 m/s
≈ 700 m/s
Therefore, the velocity of the bullet just before it hits the block is 700 m/s.
It would take more energy to reheat 12 cups because only 1 or 2 cups can fit in a microwave rather an than brewing 12 cups in a coffee pot.
Answer:
<em>The comoving distance and the proper distance scale</em>
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Explanation:
The comoving distance scale removes the effects of the expansion of the universe, which leaves us with a distance that does not change in time due to the expansion of space (since space is constantly expanding). The comoving distance and proper distance are defined to be equal at the present time; therefore, the ratio of proper distance to comoving distance now is 1. The scale factor is sometimes not equal to 1. The distance between masses in the universe may change due to other, local factors like the motion of a galaxy within a cluster. Finally, we note that the expansion of the Universe results in the proper distance changing, but the comoving distance is unchanged by an expanding universe.
It's been a while since I've studied this, but my answers would be:
13. 5730 years. The half-life of a substance is the amount of time it takes for half of it to decay, and, according to the graph, half of the substance remained at 5730 years.
14. 10740 years. According to the graph, only 25% of the carbon remained after 10740 years.
15. 15 atoms. According to the graph, only 12.5% of the carbon remained after 16110 years. 12.5% of 120 atoms is 15 atoms.
16. 1600 atoms. According to the graph, if a sample of carbon is 10740 years old, only 25% of it remains. To find the original amount, multiply the current amount by (100% / 25%), which equals 4. So, 4. 400 atoms * 4 = 1600 atoms is the original amount.
Answer : 413.44N
Here it is given that an elevator is moving down with an acceleration of 3.36 m/s² . And we are interested in finding out the apparent weight of a 64.2 kg man . For the diagram refer to the attachment .
- From the elevator's frame ( non inertial frame of reference) , we would have to think of a pseudo force.
- The direction of this force is opposite to the direction of acceleration the frame and its magnitude is equal to the product of mass of the concerned body with the acceleration of the frame .
- When a elevator accelerates down , the weight recorded is less than the actual weight .
From the Free body diagram ,
- Mass of the man = 64.2 kg
