Calculating Eraser's Distance on Friction Desk

[Matt1234]

Homework Statement

A student uses a compressed spring of force constant 22 N/m to shoot 0.0075 kg eraser across a desk. The magnitude of the force of friction on the eraser is 0.042N. How far along the horizontal desk will the eraser slideif the spring is initially compressed 3.5 cm? Use the law of conservation of energy.

Homework Equations

Ee = .5 K x^2
Ek = 0.5 m v^2
w = f d cos ()

The Attempt at a Solution

http://img189.imageshack.us/i/lastscank.jpg/

 

[bucher]

You don't need the kinetic energy equation for this problem. Set the spring energy equal to the friction energy and solve for the unknown d that the eraser would have to travel to make the equality true.

 

[nlightner]

The problem can be solved using the law of conservation of energy, which states that the total energy in a system remains constant. In this case, the initial potential energy stored in the compressed spring will be converted into kinetic energy as the eraser is launched, and then into work done against friction as the eraser slides across the desk.

To solve for the distance traveled by the eraser, we can equate the initial potential energy of the spring with the work done against friction.

Ee = Ek + W

.5 K x^2 = 0.5 m v^2 + f d cos ()

Substituting the given values, we get:

.5 (22 N/m) (0.035 m)^2 = 0.5 (0.0075 kg) v^2 + (0.042 N) d cos (0)

Solving for v, we get:

v = 3.02 m/s

Using the equation for distance traveled by an object under constant acceleration, we can solve for the distance traveled by the eraser:

d = (v^2 - u^2) / 2a

Where:
v = final velocity = 3.02 m/s
u = initial velocity = 0 m/s
a = acceleration = -0.042 N / 0.0075 kg = -5.6 m/s^2

Substituting the values, we get:

d = (3.02^2 - 0^2) / (2 * -5.6) = 0.27 m

Therefore, the eraser will slide approximately 0.27 meters along the horizontal desk. This calculation assumes that the desk is frictionless, as the force of friction is negligible compared to the force of the compressed spring. If the desk does have friction, the distance traveled by the eraser will be slightly less than 0.27 meters.