A 2.7 kg box is released on a horizontal surface with an inital speed of 2.9m/s. It moves on the surface with a deceleration of 0.27m/s^2. Calculate the kinetic friction force on the box?
To calculate the kinetic friction force on the box, we need to use the equation:
friction force (Ff) = mass (m) x acceleration due to friction (a)
First, we need to find the acceleration due to friction using the equation of motion:
final velocity (vf)^2 = initial velocity (vi)^2 + 2 x acceleration (a) x distance (d)
In this case, the box is decelerating, so the final velocity (vf) will be zero. The initial velocity (vi) is given as 2.9 m/s. We need to find the distance (d) traveled by the box.
Using the equation for distance:
d = (vf^2 - vi^2) / (2 x a)
Substituting the values, we get:
d = (0 - (2.9)^2) / (2 x (-0.27))
Simplifying further:
d = (-8.41) / (-0.54)
d ≈ 15.57 m
Now that we know the distance traveled, we can calculate the acceleration due to friction:
a = (vf^2 - vi^2) / (2 x d)
Substituting the values:
a = (0 - (2.9)^2) / (2 x 15.57)
a ≈ -0.2665 m/s^2
Next, we can calculate the friction force:
Ff = m x a
Substituting the given values:
Ff = 2.7 kg x (-0.2665 m/s^2)
Ff ≈ -0.7202 N
The negative sign indicates that the friction force is acting in the opposite direction of motion.
Therefore, the kinetic friction force on the box is approximately 0.7202 N.