Answer:
The magnitude of the force is 64.634 newtons.
Explanation:
According to the statement, the crate is a constant mass system, whose upward force is described by the following expression:
(1)
Where:
- Force, in newtons.
- Mass, in kilograms.
- Acceleration, in meters per square second.
The function acceleration is obtained by deriving the function position twice in time:
(2)
(3)
And we expand (1) by applying (3):
Where 
is the time, in seconds.
If we know that 
and 
, then the magnitude of the force is:
The magnitude of the force is 64.634 newtons.
Answer:
the speed of the car at the top of the vertical loop 
the magnitude of the normal force acting on the car at the top of the vertical loop 
Explanation:
Using the law of conservation of energy ;
The magnitude of the normal force acting on the car at the top of the vertical loop can be calculated as:
![F_{N} = \frac{mv^2_{top}}{R} \ - mg\\\\F_{N} = \frac{m(2.0 \sqrt{gR})^2}{R} \ - mg\\\\F_{N} = [(2.0^2-1]mg\\\\F_{N} = [(2.0)^2 -1) (50*10^{-3} \ kg)(9.8 \ m/s^2]\\\\](https://tex.z-dn.net/?f=F_%7BN%7D%20%3D%20%5Cfrac%7Bmv%5E2_%7Btop%7D%7D%7BR%7D%20%5C%20-%20mg%5C%5C%5C%5CF_%7BN%7D%20%3D%20%5Cfrac%7Bm%282.0%20%5Csqrt%7BgR%7D%29%5E2%7D%7BR%7D%20%5C%20-%20mg%5C%5C%5C%5CF_%7BN%7D%20%3D%20%5B%282.0%5E2-1%5Dmg%5C%5C%5C%5CF_%7BN%7D%20%3D%20%5B%282.0%29%5E2%20-1%29%20%2850%2A10%5E%7B-3%7D%20%5C%20kg%29%289.8%20%5C%20m%2Fs%5E2%5D%5C%5C%5C%5C)
