A 25 kg box is along a horizontal floor and a force of 400 N pushes the box with an angle of 50 deg with the horizontal. Starting from rest, the box achieves a velocity of 2 m/s in a time of 4 seconds. Find the coefficient of sliding friction between box and the floor.
break the pushing force into vertical and horizonal components, Fv, Fh
Fv=400sin50
Fh=400cos50
Now, write the force equation
forcetotal=ma
fh-mu*(mg+Fv)=ma solve for mu, knowing acceleration is frdom
a=changevelocity/time=2/4 m/s^2=.5m/s^2
What would be the weight of the box?
If it were not given
To find the coefficient of sliding friction between the box and the floor, we can use Newton's second law of motion.
1. First, let's break down the force acting on the box. There are two main forces at play: the applied force and the force of friction. The applied force is 400 N at an angle of 50 degrees with the horizontal. We can find the horizontal component of this force by multiplying it by the cosine of the angle:
F_applied_horizontal = 400 N * cos(50°)
2. The net force acting on the box is equal to the product of mass and acceleration. In this case, the acceleration is the change in velocity over time:
F_net = m * a
Since the box starts from rest and achieves a velocity of 2 m/s in 4 seconds, the acceleration can be calculated as:
a = (2 m/s - 0 m/s) / 4 s
3. The force of friction can be calculated using the equation:
F_friction = μ * F_normal
where μ is the coefficient of sliding friction, and F_normal is the normal force exerted by the floor on the box. The normal force is equal to the weight of the box:
F_normal = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
4. Now, we can use Newton's second law to calculate the net force:
F_net = F_applied_horizontal - F_friction
Plugging in the values we've found, the equation becomes:
m * a = F_applied_horizontal - μ * F_normal
Substituting in the values we have:
25 kg * [(2 m/s - 0 m/s) / 4 s] = F_applied_horizontal - μ * (25 kg * 9.8 m/s^2)
5. Finally, solve the equation for the coefficient of sliding friction (μ):
μ = (F_applied_horizontal - m * a) / (m * g)
Plug in the values we've calculated to find the coefficient of sliding friction.