Answer:

Explanation:
Using the tension in the spring and the force of the tension can by describe by
T = kx
, T = mg
Therefore:

With two springs, let, T1 be the tension in each spring, x1 be the extension of each spring. The spring constant of each spring is 2k so:


Solve to x1





Explanation:
For each object, the initial potential energy is converted to rotational energy and translational energy:
PE = RE + KE
mgh = ½ Iω² + ½ mv²
For the marble (a solid sphere), I = ⅖ mr².
For the basketball (a hollow sphere), I = ⅔ mr².
For the manhole cover (a solid cylinder), I = ½ mr².
For the wedding ring (a hollow cylinder), I = mr².
If we say k is the coefficient in each case:
mgh = ½ (kmr²) ω² + ½ mv²
For rolling without slipping, ωr = v:
mgh = ½ kmv² + ½ mv²
gh = ½ kv² + ½ v²
2gh = (k + 1) v²
v² = 2gh / (k + 1)
The smaller the value of k, the higher the velocity. Therefore:
marble > manhole cover > basketball > wedding ring
Answer:
10.4 m/s
Explanation:
The problem can be solved by using the following SUVAT equation:

where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
For the diver in the problem, we have:
is the initial velocity (positive because it is upward)
is the acceleration of gravity (negative because it is downward)
By substituting t = 1.7 s, we find the velocity when the diver reaches the water:

And the negative sign means that the direction is downward: so, the speed is 10.4 m/s.
Answer:
The value is
Explanation:
From the question we are told that
The mass of the car is
The acceleration is 
Generally the net force applied on the rope is mathematically represented as

Here W is the weight of the car which is evaluated as
=> 
=> 
Generally the net force can also be mathematically represented as
So

=> 
=>