**Answer:**

8.9

**Explanation:**

We can start by calculating the initial elastic potential energy of the spring. This is given by:

(1)

where

k = 35.0 N/m is the initial spring constant

x = 0.375 m is the compression of the spring

Solving the equation,

Later, the professor told the student that he needs an elastic potential energy of

U' = 22.0 J

to achieve his goal. Assuming that the compression of the spring will remain the same, this means that we can calculate the new spring constant that is needed to achieve this energy, by solving eq.(1) for k:

Therefore, Tom needs to increase the spring constant by a factor:

**Answer:**

d=1.25 m

**Explanation:**

fd=.5mv2-.5mv1; 10(d)=.5(50)(.5)-0; 10(d)=12.5; d=12.5/10; d=1.25 m

The second object exerts an equal and opposite force on the first object.

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Answer:

w = 6.325 rad/s

Explanation:

Given the following data;

Mass = 2kg

Radius, r = 10m

Centripetal force = 800N

To find the angular velocity of the car;

First of all, we would use the following formula to solve for the speed of the car;

Centripetal force = mv²/r

800 = 2*v²/10

Cross-multiplying, we have;

8000 = 2v²

4000 = v²

Taking the square root of both sides, we have;

v = √4000

v = 63.25 m/s

Next, we find the angular velocity, w using the formula below;

w = v/r

w = 63.25/10

w = 6.325 rad/s