The block in the figure below lies on a horizontal frictionless surface and is attached to the free end of the spring, with a spring constant of 60 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 2.7 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops.
Assume that the stopping point is reached.
(a) What is the position of the block?
(b) What is the work that has been done on the block by the applied force?
(c) What is the work that has been done on the block by the spring force?
Im doing this online and I got these answers:
a.) .045m
b.) 0.122 J
c.) -0.06075 J
The website says they are wrong but I have absolutely no clue why, especiall for part A, its a joke. All you need to do is plug in F = -kx and they give you force and k but it still says its wrong.
you need to take the integral of the force to find the work and then solve for x.
&int -kx = &int 2.7
(-kx2) = 2.7x
solve for x
sorry, didn't write that properly..
(kx2)/2 = 2.7x
you solve for work because the block started from rest and ended at rest. KEf - KEi = Worka + (-Ws)
where Worka = the Work done by the applied force
To solve these questions, you need to apply the concepts of force, work, and energy. Let's go through each part step by step:
(a) To find the position of the block, you need to use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. In equation form, this is expressed as F = -kx, where F is the force, k is the spring constant, and x is the displacement.
Given that an applied force of 2.7 N is pulling the block, we can set up the equation: 2.7 N = -kx.
Since the block stops at the stopping point, the net force acting on the block is zero. This means that the force exerted by the spring must be equal in magnitude but opposite in direction to the applied force. So we can rewrite the equation as -2.7 N = -kx.
Next, we know that the spring constant (k) is given as 60 N/m. Plugging in this value, we get -2.7 N = -(60 N/m) * x.
Solving for x, we find that x = 2.7 N / (60 N/m) = 0.045 m.
Therefore, the position of the block is 0.045 m.
(b) To find the work done by the applied force, we can use the formula W = F * d * cos(theta), where W is the work done, F is the force, d is the displacement, and theta is the angle between the force and displacement vectors.
In this case, the applied force is constant, and the displacement is equal to x = 0.045 m (as found in part a). Since the applied force and the displacement are in the same direction, the angle theta is 0 degrees, and the cosine of 0 degrees is 1.
Using the formula, we have W = (2.7 N) * (0.045 m) * cos(0°) = 0.1215 J ≈ 0.122 J.
Therefore, the work done by the applied force is approximately 0.122 J.
(c) To find the work done by the spring force, we can use the formula W = (1/2)kx^2, where W is the work done, k is the spring constant, and x is the displacement.
In this case, the spring force is acting in the opposite direction to the displacement, so the angle theta is 180 degrees. The cosine of 180 degrees is -1.
Using the formula, we have W = (1/2)(60 N/m)(0.045 m)^2 * (-1) = -0.06075 J.
Therefore, the work done by the spring force is -0.06075 J.
So, the correct answers are:
(a) The position of the block is 0.045 m.
(b) The work done on the block by the applied force is approximately 0.122 J.
(c) The work done on the block by the spring force is -0.06075 J.
If the website marks them as wrong, it could be due to rounding differences or an error in their answer key. I would suggest rechecking your calculations and contacting your instructor or the website for further clarification.