A 5.84 box sits on a ramp that is inclined at 35.2 above the horizontal. The coefficient of kinetic friction between the box and the ramp is 0.27. What horizontal force is required to move the box up the incline with a constant acceleration of 4.30 ?
N=m•g•cosα+F•sinα
ma=F•cosα-F(fr)-mgsinα =
=F•cosα - μN- mgsinα=
= F•cosα – μ(m•g•cosα+F•sinα) - mgsinα,
ma = F•cosα – μ•m•g•cosα - μ•F•sinα - mgsinα,
F• (cosα -μ•sinα) = m(a+g•sinα+μ•g•cosα),
F= m(a+g•sinα+μ•g•cosα)/ (cosα -μ•sinα).
Dimensions must be provided with your numbers.
A 5.84kg box sits on a ramp that is inclined at 35.2degrees above the horizontal. The coefficient of kinetic friction between the box and the ramp is 0.27. What horizontal force is required to move the box up the incline with a constant acceleration of 4.30m/s square
To find the horizontal force required to move the box up the incline with a constant acceleration, you can follow these steps:
Step 1: Resolve the forces
First, resolve the forces acting on the box into their components. You have the weight force (mg), the normal force (N), the friction force (f), and the applied force (F).
Since the box is on an inclined plane, the weight force can be resolved into two components: one perpendicular to the incline (N), and the other parallel to the incline (mg*sinθ). Here, θ represents the angle of inclination, which is given as 35.2 degrees.
Step 2: Calculate the normal force
The normal force (N) is equal to the component of the weight force perpendicular to the incline. Using trigonometry, you can calculate it as:
N = mg*cosθ
Step 3: Calculate the friction force
The friction force (f) can be determined using the formula:
f = μ*N
where μ is the coefficient of kinetic friction. In this case, it is given as 0.27.
Step 4: Determine the net force
The net force acting on the box is the difference between the applied force and the friction force in the horizontal direction. Therefore:
Net force (Fnet) = F - f
Step 5: Calculate the required force
Since the box is moving up the incline with constant acceleration, the net force is equal to the product of the box's mass (m) and the desired acceleration (a):
Fnet = m*a
By setting Fnet equal to the calculated net force from step 4, you can solve for the applied force (F):
F = Fnet + f
Plugging in the given values, you can calculate the horizontal force required.