How do you determine whether a line is parallel to a plane? What are some examples?
If a line is parallel to a plane, it will be perpendicular to the plane’s normal vector (just like any other line contained within the plane, or parallel to the plane).(Note that I’m using “perpendicular” here, not in the sense that they intersect, necessarily, but in the sense that their vectors would be at 90 degrees if they were placed next to one another)To find if two vectors are perpendicular, just take their dot product. If it equals 0, then they are perpendicular.So, for example, if we have the plane: 2x + 3y - 4z = 7 (normal vector here would be <2,3,-4>)And we want to find out if the line: x=2+t, y=3–2t, z=5-t, is parallel to it, we just need the dot product of the line’s vector (<1, -2, -1>) and the plane’s normal vector.<1, -2, -1> DOT <2, 3, -4> = 1*2 + -2*3 + -1*-4 = 2 - 6 + 4 = 0So in this case, the line & plane are parallel.If we want to use the same plane, but compare it to the line: x=4+2t, y=3+6t, z=5+9t, then we will get:<2, 6, 9> DOT <2, 3, -4> = 2*2 + 6*3 + 9*-4 = 4 + 18 - 36 = -14So we can see these two will not be parallel.
A 4.1- cm-radius ball rolls down an inclined plane from rest at the top. The angular acceleration of the roll?
A 4.1- cm-radius ball rolls down an inclined plane from rest at the top. The angular acceleration of the rolling ball about its center is 210 rad/s2, and its angular speed at the bottom is 64.4 rad/s. How long is the plane?
A 2 kg block slides down on an inclined plane and reaches the bottom with speed 4 m/s.?
A 2 kg block slides down on an inclined plane and reaches the bottom with speed 4 m/s. How much work does the force of friction do if the block starts from rest at a height of 1.5 m. Please Help Thank you
A block weighing 82.5 N rests on a plane inclined at 25.0° to the horizontal.?
I will assume that the force F is pushing at an angle that is positive w/r/t the horizontal plane, such that it is pushing the block up the plane and reducing the normal force of the block. If this is incorrect, it is simple to change the sign of the vertical component of the force and recalculate the numbers. The normal force of the block is a bit tricky since the components of the force F must be decomposed into the part that is perpendicular to the plane and the part that is parallel to the plane. F subtends an angle w/r/t the plane of 40-25 degrees, or 15 degrees. The part that is perpendicular and upward is sin(15)*F which is part of the normal force on the interface of the plane and the block adding gravity, the normal force is cos(25)*m*g-sin(15)*F 733.5-sin(15)*F and the part that is parallel is cos(15)*F the part of gravity resisting the force is sin(25)*m*g =342 N a) the question is asking what value of F will balance the gravity force at the threshold of static friction downward on the plane? Looking at a FBD The force upward on the plane plus the static friction oppose the gravitational pull down slope 342=(733.5-sin(15)*F)*.342 +cos(15)*F (342-733.5.342)/ (cos(15)-sin(15)*.342)=F F=104 N b) This is asking what will exactly balance the gravity force at the threshold of static friction upward on the plane Now the FBD has F upward has to overcome gravity and the static friction force cos(15)*F= 342+(733.5-sin(15)*F)*.342 F(cos(15)+sin(15)*.342)= 342+733.5*.342 F=(342+733.5*.342)/ (cos(15)+sin(15)*.342) F=562 N c) This is asking what will exactly balance the gravity and the kinetic friction same equation as b, except use u kinetic F=(342+733.5*.156)/ (cos(15)+sin(15)*.156) F=453.6 N j
How far up the incline will the block move before coming to rest?
The first part tells you enough to compute the force of friction f=12.9*sin(22.6) Then using conservation of energy .5*12.9*4.8^2= 12.9*D*sin(22.6)*(9.8*sin(22.6)-1) where D is the distance j
A 4 kg block is lowered down a 37 degrees incline a distance of 5 m form point A to point B.?
A 4 kg block is lowered down a 37 degrees incline a distance of 5 m form point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B. The kinetic energy of the block at A is 10 J and at B is 20 J. How much work is done on the block by the force of friction between A and B?