Force & Tension: Solving 2 Problems

[BriannaUND]

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!

 

[lightgrav]

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.

 

[quicknote]

For the first problem, you are correct in your calculation of the force of gravity (Fg). In order to calculate the average force acting on the ball by the sand, you will need to use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration can be calculated using the formula a = vf^2 - vi^2 / 2d, where vf is the final velocity (which is 0 since the ball is stopped by the sand), vi is the initial velocity (which is the velocity at which the ball is dropped, which can be calculated using the equation vi = √(2gh), where g is the acceleration due to gravity and h is the height from which the ball was dropped), and d is the distance the ball traveled (which is 5.0 cm). Once you have calculated the acceleration, you can use the F = ma equation to find the average force acting on the ball by the sand.

For the second problem, you are correct in your calculation of the tension in the string (T). However, the answer in the back of the book is most likely taking into account the weight of m1 as well. In order to calculate the tension in the string, you need to consider the forces acting on m1 and m2. In this case, m1 is being pulled down the incline by its weight (mg) and being held back by the tension in the string (T). So the equation would be mg - T = ma, where m is the mass of m1, g is the acceleration due to gravity, and a is the acceleration of the system (which is given as 1.2 m/s2). You can then solve for T, which should give you the correct answer of 21 N.