A Block weighing 72.2 N rests on a plane inclined at 20.0 deg. to the horizontal. The coefficients of static and kinetic friction are 0.22 and 0.12 resp.
What is the minimum magnitude of F that will start the block moving up the plane? (I also got 9,74 N for this.. but wrong answer.)
As well, what is the magnitude of F required to move the black up the plane at constant velocity? (I got 16.5 N for this... but it was also the wrong answer)
help please!!!
I assume F is up the plane, parallel to the plane.
Forces on the block, using Up the plane as positive.
F -mgsinTheta - mu*mgCosTheta=0
I don't get your answers..
To solve this problem, we need to calculate the various forces acting on the block. Let's analyze each part separately.
1. Minimum magnitude of force (F) to start the block moving up the plane:
First, we need to find the force of static friction to determine the minimum force required.
The force of static friction (Fs) can be calculated using the formula:
Fs = coefficient of static friction * normal force
Normal force (N) can be found by decomposing the weight of the block into components perpendicular and parallel to the inclined plane.
N = weight of the block * cos(angle of incline)
Weight of the block is the force acting vertically, which is the product of its mass (m) and gravitational acceleration (g).
Weight of the block = m * g
Substituting the given values into the equation:
Weight of the block = 72.2 N
Angle of incline = 20.0 degrees
Coefficient of static friction = 0.22
Now, we can calculate the normal force using the formula:
N = 72.2 N * cos(20.0 degrees)
Next, we can find the force of static friction:
Fs = 0.22 * N
Finally, the minimum magnitude of force required to start the block moving up the plane is equal to the force of static friction:
F = Fs
To calculate the value, use the above steps and plug them into the equation.
Now, let's move on to the second part of the problem.
2. Magnitude of force (F) required to move the block up the plane at constant velocity:
Once the block is in motion, the force of kinetic friction comes into play. The force of kinetic friction (Fk) can be calculated using the same formula as the force of static friction, but with the coefficient of kinetic friction.
Fk = coefficient of kinetic friction * normal force
Using the same approach as before, we can find the normal force and then calculate the kinetic friction.
Now that we have the force of kinetic friction, the magnitude of the force required to move the block up the plane at constant velocity is given by balancing the applied force (F) with the force of kinetic friction:
F = Fk
Again, use the above steps to calculate the value.
It is important to double-check your calculations and make sure you are using the correct values for the coefficient of friction and the angle of incline.