Kinetic energy/circular motion problems

[physixnot4me]

hi! I am currently doing more homework problems, and getting stuck on questions like these:

(1) the only force acting on a 2kg body as it moves along the x-axis is given by F=(12-2x)N where x is in m. the velocity of the body at x=2m is 5.5i m/s. what is the maximum kinetic energy attained by the body?

KE= 1/2mv^2 ... how am i to determine velocity if 5.5i m/s... i is a unit vector, how am i supppose to solve for MAX. kinetic energy?

(3) if the resultant force acting on a 2kg object is equal to (3i +4j) N, what is the change in kinetic energy as the object moves from (7i-8j)m to (11i-5j)m?

again, with vector units, how do include them in my calculations?

(2) a split highway has a number of lanes for traffic. for traffic going in one direction, the radius for the inside of the curve is 1/2 the radius for the outside. one car, Car A, travels on the inside while another car of equal mass, car B travels at equal speed on the outside of the curve. which statement about resultant forces on the cars is correct?

a) The force on A is four times the force on B.
b) The force on B is half the force on A.
c) The force on A is half the force on B.
d) The force on B is four times the force on A.
e) There is no net resultant force on either as long as they stay on the road while turning.

(4) how much work is done by a person lifting a 2kg object from the bottom of a well at a constant speed of 2 m/s for 5.0 sec?

how would the work formula apply here?

any comments would be appreciated, the more understanding i get, the better off i am. thanks.

 

[Päällikkö]

(1)
I hope this isn't too much help.
Newton II?
Definition of acceleration?

(3)
How is work defined (think line integral)?

(2)
Centripetal acceleration?

(4)
Again, the definition of work?

 

[quicknote]

I can provide some guidance on how to approach these types of problems. Firstly, it is important to remember that in physics, vectors (such as the velocity in problem 1 and the resultant force in problem 3) have both magnitude and direction. In order to solve these problems, you will need to consider both the magnitude and direction of these vectors.

For problem 1, you are given the velocity of the body at a specific point (x=2m) and the force acting on it at that point. To determine the maximum kinetic energy, you will need to use the formula KE=1/2mv^2, where m is the mass and v is the velocity. In this case, you will need to use the magnitude of the velocity (5.5m/s) and the mass (2kg) to calculate the maximum kinetic energy.

For problem 3, you are given the resultant force acting on the object at two different points. In order to calculate the change in kinetic energy, you will need to use the formula ΔKE=∫Fdx, where F is the force and dx is the displacement. In this case, you will need to integrate the force with respect to displacement in order to find the change in kinetic energy.

For problem 2, you will need to use the concept of centripetal force in circular motion. The force on an object moving in a circular path is equal to the mass of the object times its centripetal acceleration (F=ma). Since both cars have the same mass and are traveling at the same speed, the only difference is the radius of their paths. This means that the force on the car on the inside of the curve will be greater, since it has a smaller radius and therefore a larger centripetal acceleration.

For problem 4, you will need to use the formula W=Fd, where W is the work done, F is the force applied, and d is the displacement. In this case, the force being applied is equal to the weight of the object (mg), so you can use the formula W=mgd to calculate the work done.

In general, it is important to carefully read the problem and identify the relevant equations and variables that you will need to solve it. Remember to always include units in your calculations and to pay attention to the direction of vectors. With practice and a solid understanding of the concepts, you will become more proficient at solving these types