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09) An object of weight 'W' is resting on an inclined plane inclined at 0°to the horizontal. Show that the horizontal W(sin 0 + µ̟cos 0) force needed to just push the block up the inclined plane is F= where u is the coefficient of (cos0 – µ sin O) friction.

09) An object of weight 'W' is resting on an inclined plane inclined at 0°to the horizontal. Show that the horizontal W(sin 0 + µ̟cos 0) force needed to just push the block up the inclined plane is F= where u is the coefficient of (cos0 – µ sin O) friction.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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09) An object of weight 'W' is resting on an inclined plane inclined at 0" to the horizontal. Show that the horizontal W (sin 0 + µcos0) (cos 0-usin 0) force needed to just push the block up the inclined plane is F= where u is the coefficient of friction. 10) A particle is projected along a rough inclined plane straight up with kinetic energy E. Show that the work done Εμcosθ sin θ+ μcos against friction before the particle comes to rest is where u is the coefficient of friction and 0 is the inclination of the plane to the horizontal. 11) A block slides down an inclined plane with a constant velocity 'v'. It is then projected up the plane with an initial u? velocity 'u'. Show that the distance it can rise before coming to rest is 4g sin 0
Transcribed Image Text:09) An object of weight 'W' is resting on an inclined plane inclined at 0" to the horizontal. Show that the horizontal W (sin 0 + µcos0) (cos 0-usin 0) force needed to just push the block up the inclined plane is F= where u is the coefficient of friction. 10) A particle is projected along a rough inclined plane straight up with kinetic energy E. Show that the work done Εμcosθ sin θ+ μcos against friction before the particle comes to rest is where u is the coefficient of friction and 0 is the inclination of the plane to the horizontal. 11) A block slides down an inclined plane with a constant velocity 'v'. It is then projected up the plane with an initial u? velocity 'u'. Show that the distance it can rise before coming to rest is 4g sin 0
6:23 PM | 10.7KB/s © M 65 mfewpe - 11 - 2020 SADHANA SAXENA EQUILIBRIUM 01) A mass of 10kg is suspended by a thread and is pulled horizontally by a horizontal force of 98N so as to make the thread to come to rest at an angle of 0° to the vertical. Calculate the angle 0°. 02) A body is suspended by a string and is pulled by a spring balance till the string makes an angle of 60° with the vertical. If the reading of the spring balance is 18kgwt, calculate the tension in the string and the weight of the body. 03) A mass of 30gms. Suspended with a thread is pulled horizontally to make the thread to come to rest at an angle of 30° to vertical. Calculate the pulling force P required and also in the tension in the string. 04) Find the tensions in each cord in the following cases. Let the weight of the suspended body be 20ON. 05) Find the weight, W of the suspended body in the following cases. The tension in a certain string is given in the figure. 30 45 45 45 53 53 60 200 N 200 N 200 N 30 A 43 Tc= 20N TA= 12N T= 10N T= 1ON %3D FRICTION 01) A block rests on a horizontal surface and weighs 20N. A horizontal force can be increased to 8N before the block starts to slide along the horizontal surface. A force of 7N will keep the block in uniform motion, once it has been set in motion. Find the coefficient of static and kinetic friction. What is the force of friction when a horizontal force of 5N is applied to it? 02) A body of mass 50kg is kept on a horizontal surface of coefficient of static friction 0·5. Find the least horizontal force required to start the motion. If now the body is slightly displaced and the same force continues to act, find the acceleration with which it moves. (Coefficient of kinetic friction is 0 - 48) 03) Find the least pulling force P which acting at an angle of 45º with the horizontal surface. The coefficient of friction V3 between the two surfaces in contact is 04) A block of wood of mass 150gms rests on an inclined plane. If the coefficient of static friction is 0.3 find a) the greatest angle to which the plane may be tilted without the block moving b) the force parallel to the plane, necessary to prevent slipping when the angle of the plane with the horizontal is 30°. 05) A block of mass 2kg slides down an inclined plane, which makes an angle of 30° to the horizontal. If the coefficient of friction is 3% what force should be applied to the block so that the block a) moves down without any sadhund Sana acceleration b) moves up without any acceleration? Calculate the ratio of the powers needed in the above two cases if the block moves with the same speed in both the cases. 06) How long will it take a wooden block to slide from rest a distance of 3m down a rough inclined plane at 30° to the horizontal? (The coefficient of kinetic friction is 0·2) 07) A horizontal force of 12 N pushes a block of weight 5N against a vertical wall. The coefficient of static friction between the block and the wall is 0-6. What is a) the normal reaction b) the frictional force? Does the block move? 08) A block of mass 2kg rests on a rough inclined plane at 30° with the horizontal. Calculate the frictional force. The coefficient of friction is 0.7. 09) An object of weight 'W' is resting on an inclined plane inclined at 0° to the horizontal. Show that the horizontal W (sin 0 + µcos0) force needed to just push the block up the inclined plane is F= where u is the coefficient of (cos0 – u sin 0) friction. 10) A particle is projected along a rough inclined plane straight up with kinetic energy E. Show that the work done Εμcosθ sin 0+µcos0 against friction before the particle comes to rest is where u is the coefficient of friction and 0 is the inclination of the plane to the horizontal. 11) A block slides down an inclined plane with a constant velocity 'v'. It is then projected up the plane with an initial u? velocity 'u'. Show that the distance it can rise before coming to rest is 4g sin 0 LAWS OF MOTION 01) A scooter of mass 120gms. Is moving with a uniform velocity of 108kmhr -!. Calculate the force required to stop the vehicle in 10sec. 02) Two forces one of which is thrice the other act on a particle at right angles to one another and are such that if the smaller force is doubled and 8kgwt added to the other, the direction of the resultant is unchanged. Determine the magnitudes of the two forces. 03) A body of mass 2kg is acted upon by two forces each of magnitude 1N making an angle of 60° with respect to each other. Calculate the acceleration produced in the body. 04) A bullet of mass 5gm moving with a velocity of 3m/s hits a wall and pierces to a depth of 15mm, Determine the force exerted by the wall on the bullet.
Transcribed Image Text:6:23 PM | 10.7KB/s © M 65 mfewpe - 11 - 2020 SADHANA SAXENA EQUILIBRIUM 01) A mass of 10kg is suspended by a thread and is pulled horizontally by a horizontal force of 98N so as to make the thread to come to rest at an angle of 0° to the vertical. Calculate the angle 0°. 02) A body is suspended by a string and is pulled by a spring balance till the string makes an angle of 60° with the vertical. If the reading of the spring balance is 18kgwt, calculate the tension in the string and the weight of the body. 03) A mass of 30gms. Suspended with a thread is pulled horizontally to make the thread to come to rest at an angle of 30° to vertical. Calculate the pulling force P required and also in the tension in the string. 04) Find the tensions in each cord in the following cases. Let the weight of the suspended body be 20ON. 05) Find the weight, W of the suspended body in the following cases. The tension in a certain string is given in the figure. 30 45 45 45 53 53 60 200 N 200 N 200 N 30 A 43 Tc= 20N TA= 12N T= 10N T= 1ON %3D FRICTION 01) A block rests on a horizontal surface and weighs 20N. A horizontal force can be increased to 8N before the block starts to slide along the horizontal surface. A force of 7N will keep the block in uniform motion, once it has been set in motion. Find the coefficient of static and kinetic friction. What is the force of friction when a horizontal force of 5N is applied to it? 02) A body of mass 50kg is kept on a horizontal surface of coefficient of static friction 0·5. Find the least horizontal force required to start the motion. If now the body is slightly displaced and the same force continues to act, find the acceleration with which it moves. (Coefficient of kinetic friction is 0 - 48) 03) Find the least pulling force P which acting at an angle of 45º with the horizontal surface. The coefficient of friction V3 between the two surfaces in contact is 04) A block of wood of mass 150gms rests on an inclined plane. If the coefficient of static friction is 0.3 find a) the greatest angle to which the plane may be tilted without the block moving b) the force parallel to the plane, necessary to prevent slipping when the angle of the plane with the horizontal is 30°. 05) A block of mass 2kg slides down an inclined plane, which makes an angle of 30° to the horizontal. If the coefficient of friction is 3% what force should be applied to the block so that the block a) moves down without any sadhund Sana acceleration b) moves up without any acceleration? Calculate the ratio of the powers needed in the above two cases if the block moves with the same speed in both the cases. 06) How long will it take a wooden block to slide from rest a distance of 3m down a rough inclined plane at 30° to the horizontal? (The coefficient of kinetic friction is 0·2) 07) A horizontal force of 12 N pushes a block of weight 5N against a vertical wall. The coefficient of static friction between the block and the wall is 0-6. What is a) the normal reaction b) the frictional force? Does the block move? 08) A block of mass 2kg rests on a rough inclined plane at 30° with the horizontal. Calculate the frictional force. The coefficient of friction is 0.7. 09) An object of weight 'W' is resting on an inclined plane inclined at 0° to the horizontal. Show that the horizontal W (sin 0 + µcos0) force needed to just push the block up the inclined plane is F= where u is the coefficient of (cos0 – u sin 0) friction. 10) A particle is projected along a rough inclined plane straight up with kinetic energy E. Show that the work done Εμcosθ sin 0+µcos0 against friction before the particle comes to rest is where u is the coefficient of friction and 0 is the inclination of the plane to the horizontal. 11) A block slides down an inclined plane with a constant velocity 'v'. It is then projected up the plane with an initial u? velocity 'u'. Show that the distance it can rise before coming to rest is 4g sin 0 LAWS OF MOTION 01) A scooter of mass 120gms. Is moving with a uniform velocity of 108kmhr -!. Calculate the force required to stop the vehicle in 10sec. 02) Two forces one of which is thrice the other act on a particle at right angles to one another and are such that if the smaller force is doubled and 8kgwt added to the other, the direction of the resultant is unchanged. Determine the magnitudes of the two forces. 03) A body of mass 2kg is acted upon by two forces each of magnitude 1N making an angle of 60° with respect to each other. Calculate the acceleration produced in the body. 04) A bullet of mass 5gm moving with a velocity of 3m/s hits a wall and pierces to a depth of 15mm, Determine the force exerted by the wall on the bullet.
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