1st question: I was solving a question and I was asked the work done by friction. It is natural that work done by friction (a retarding force)should be negative and in my answer it was. However, just to be sure, work can be negative?

2nd question: A block of m = 2.00kg is moving a long a frictionless horizontal surface. The block reaches the relaxed spring (x ini. = 0) with an initial velocity of 6 m/s and compresses it to x final = 0.150m. At this value of compression, the speed of the block is reduced to v final = 4.00 m/s.

a) during this process, what is the change in Kinetic energy of the block?

sol) mv2(f)/2 - mv2 (i)/2 (correct?)

B) How much work has been done by the spring force on the block.

W(s)= mv2(i)/2 - mv2(f)/2

c) What is the spring constant of this spring. (hint: use work-kinetic energy theorem)

would it be x * whatever I get for part A?

Do any of the above answers make sense?

work done is negative when work is done on the system.

a correct
b correct
c No. change KE= 1/2 k x^2 solve for k.

1st question: Yes, work can be negative. In the case of friction, when an object is moving in the opposite direction of the applied force, the work done by friction is negative. This is because friction is acting against the direction of motion, resulting in the object losing energy. So, it is natural for the work done by friction to be negative.

2nd question:
a) To calculate the change in kinetic energy of the block, you can use the equation:
ΔKE = KE final - KE initial = 1/2 m v final^2 - 1/2 m v initial^2
So, your solution: mv final^2/2 - mv initial^2/2 is correct.

b) To find the work done by the spring force on the block, you can use the equation:
W(spring) = ΔKE = KE initial - KE final = 1/2 m v initial^2 - 1/2 m v final^2
Therefore, your solution: mv initial^2/2 - mv final^2/2 is correct.

c) The spring constant (k) can be determined using the work-kinetic energy theorem, which states that the work done by a force is equal to the change in kinetic energy. In this case, the work done by the spring force is equal to the change in kinetic energy.
So, to find the spring constant, you need to solve the equation: ΔKE = 1/2 k x^2, where ΔKE is the change in kinetic energy and x is the compression of the spring.
Your solution of using x multiplied by the answer calculated in part a (mv final^2/2 - mv initial^2/2) is incorrect.
Instead, you need to rearrange the equation: k = 2ΔKE / x^2. Substitute the values of ΔKE calculated in part a and the given value of x (0.150m) to determine the spring constant.