Learn to Create a Robotic Device Using Arduino in the Free Webinar. Register Now
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Free webinar on Robotics (Block Chain) Learn to create a Robotic Device Using Arduino
30th Jan @ 5:00PM for Grade 1 to 10
If a pushing force making an angle @ with horizontal is applied on a block of mass m placed on a horizontal table and angle of friction is b then the minimum magnitude of force required to move the block is what??? If a pushing force making an angle @ with horizontal is applied on a block of mass m placed on a horizontal table and angle of friction is b then the minimum magnitude of force required to move the block is what???
Look at the figures is attachments. Here FF is the force applied and ff is force due to frictionF(cos α)=f cos β F (cos α)= f coβ (1)Also,f = μ N f = μ N (2)where, μμ is the coefficient of friction and NN is the normal reaction by the floor on the block.By force balance on the block along the vertical direction we getN= F sin α + f sin β + mg N=F sin α +f sin β + mg (3)subtracting 2 and 3 we getN = F sin α + mg ( 1 − μ sin β ) N = F sin α + mg ( 1 − μ sin β) (4)Now subtracting 2 and 4 we getF cos α = μ F sin α + mg ( 1 − μ sin β ) cos β F cos α = μ F sin α + mg ( 1 − μ sin β ) cos βF cos α ( 1− μ sin β ) =μ cos β ( F sin α + mg ) F cos α ( 1 – μ sin β ) = μ cos β ( F sin α + mg )F cos α ( 1 − μ sin β ) = F μ cos β sin α + μ mg cos β F cos α ( 1−μ sin β) =F μ cos β sin α+ μ mg cos βF [cos α− μ cos α sin β− μ cos β sin α ]= μ mg cos β F [ cos α –μ cos α sin β− μ cos β sin α ] = μ mg cos βF = μ mg cos β cos α – μ ( cos α sin β + cos β sin α ) F = μ mg cos β cos α – μ ( cos α sin β + cos β sin α )F = μ mg cos β cos α – μ sin ( α + β ) F = μ mg cos β cos α – μ sin ( α + β )since sin ( α + β ) = cos α sin β + cos β sin α sin ( α + β ) = cos α sin β + cos β sin α.F = F min = μ mg cos β cos α – μ sin ( α + β )F = F min = μ mg cos β cos α – μ sin ( α + β ).
Look at the figures is attachments. Here FF is the force applied and ff is force due to friction
F(cos α)=f cos β F (cos α)= f coβ (1)Also,f = μ N f = μ N (2)where, μμ is the coefficient of friction and NN is the normal reaction by the floor on the block.By force balance on the block along the vertical direction we getN= F sin α + f sin β + mg N=F sin α +f sin β + mg (3)subtracting 2 and 3 we getN = F sin α + mg ( 1 − μ sin β ) N = F sin α + mg ( 1 − μ sin β) (4)Now subtracting 2 and 4 we getF cos α = μ F sin α + mg ( 1 − μ sin β ) cos β F cos α = μ F sin α + mg ( 1 − μ sin β ) cos βF cos α ( 1− μ sin β ) =μ cos β ( F sin α + mg ) F cos α ( 1 – μ sin β ) = μ cos β ( F sin α + mg )F cos α ( 1 − μ sin β ) = F μ cos β sin α + μ mg cos β F cos α ( 1−μ sin β) =F μ cos β sin α+ μ mg cos βF [cos α− μ cos α sin β− μ cos β sin α ]= μ mg cos β F [ cos α –μ cos α sin β− μ cos β sin α ] = μ mg cos βF = μ mg cos β cos α – μ ( cos α sin β + cos β sin α ) F = μ mg cos β cos α – μ ( cos α sin β + cos β sin α )F = μ mg cos β cos α – μ sin ( α + β ) F = μ mg cos β cos α – μ sin ( α + β )since sin ( α + β ) = cos α sin β + cos β sin α sin ( α + β ) = cos α sin β + cos β sin α.F = F min = μ mg cos β cos α – μ sin ( α + β )
F = F min = μ mg cos β cos α – μ sin ( α + β ).
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -