Force & Tension: Solving 2 Problems

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The discussion revolves around two physics problems involving force and tension. For the first problem, a 0.2 kg ball dropped from 10 m creates a 5 cm impression in the sand, and the average force acting on the ball by the sand needs to be calculated, with confusion regarding the normal force. The second problem involves a pulley system with two blocks, where the calculated tension of 3 N is incorrect according to the book, which states it should be 21 N due to the need to counteract gravitational forces. Additional calculations involving acceleration and energy concepts are suggested to clarify the solutions. Understanding the forces at play is crucial for accurately solving both problems.
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I am having some trouble with two problems- thanks for any help!
71) A .2kg ball is dropped from 10 m above the beach, leaving an impression in the sand 5.0 cm deep. What is the average force acting on the ball by the sand?
So far I have converted 5.0cm to .05m. I calculated Fg= .2 kg (9.8m/s2) = 1.96 N. Now I am confused as to how I should calculate the normal force of the sand.
73) On an inclined plane (with angle of 37 degrees) a pulley is holding block m1 on the incline and block two is hanging on the other side. The weights of the blocks are m1= 3.0kg, m2= 2.5kg. What is the tension in the string if the acceleration is 1.2 m/s2?
I calculated T= m2a = (2.5kg)(1.2m/s2) = 3 N but the answer in the back of the book says it should be 21 N?
Thanks again for the help- I really appreciate it!
 
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73: your 3N is the TOTAL (net) Force.
gravity contributes about 25N
and the string has to cancel all but 3N of it.

72: it falls 10m from rest : ½ at^2 to find t,
then get v = a t just before hitting the sand.
The Force by the sand has to cangel gravity
and have enough left over to "decelerate" it.
Do you know energy? otherwise, v^2 = 2ax.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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