An empty coal-car mass (20,000kg) of a train coasts along at 10m/s. An unfortuna

Question

An empty coal-car mass (20,000kg) of a train coasts along at 10m/s. An unfortunate 3000kg elephant falls from a bridge and drops vertically into the car. Determine the speed of the car immediately after the elephant is added to its contents. (ANS= 8.7m/s)

An astronaut lands on a previously unknown planet of radius 2350km and she measures the acceleration of gravity to be 3.20m/s^2. A) what is the mass of this new planet? (ANSWER .26*10^24KG) B) what does the astronaut weigh on this new planet if she weighs 382N on earth? (ANSWER 125N)

A girl weighing 450N sits on one end of a seesaw that is 3.0m long and is pivoted 1.3m from the girl. if the seesaw is just balanced when a boy sits at the opposite end, what is his weight? Neglect the weight of the seesaw. (ANSWER 344N)

two children, each of mass 20.0kg, ride on the perimeter of a small merry-go-round that is rotating at the rate of 1.0 revolution every 4.0s. The merry-go-round is a disk of mass 30kg and radius 3.0m. The children now both move halfway in toward the center to positions 1.5m from the axis of rotation. Calculate the kinetic energy before and after and the final rate of rotation. Explain any changes in energy. (ANSWER Ko=0.61KJ; Kf=1.3KJ; f=0.55H2; childred did the work)

The answers are givien but i'm just not sure how to do the work to get to the answer. Please help!!

Explanation / Answer

1. using conservation of momentum (m*v=constant)

20,000*10=(20,000+3000)*V

=> v= 20000*10/23000=8.7 m/s

2. acceleration a=G*M/R^2

=> M= a*R^2/G= 3.2*(2350*1000)^2/6.67*10^(-11) =0.26*10^24KG

mass = 382/g=382/9.8=38.98 kg

so weight at this planet = 38.98*a=38.98*3.2=125N

3. apply moment balance about pivot point,

450*1.3=W*(3-1.3)

=> W=450*103/1.7= 344N

4. In this question first find velocity using revolution per second(N) = 2*pi*N*r

and then apply the formula of K.E. =1/2*m*v^2 you will get the answer

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