Problem 3. (25 pts) A horizontal force Fp pushes a block of...

Problem 3. (25 pts) A horizontal force Fp pushes a block of mass m, starting from rest, a distance d up along a frictionless ramp inclined at angle ?. See the diagram. Write the equations used in your solutions before substituting numbers. A) (5 pts) Draw a free body diagram and label all forces acting on the box. Include a coordinate system. m = 18 kg, Fp = 150 N, d = 2.5 m, ? = 27° B) (5 pts) How much work is done by Fp, the horizontal force, pushing the block up the ramp during the displacement? C) (5 pts) How much work is done by gravity on the block during the displacement up the ramp? D) (2 pts) How much work is done by the normal force? E) (8 pts) Use work-kinetic energy to find the speed of the block after this displacement.

Transcript

00:01 A box here is being pushed upward along a ramp that is inclined to 27 degrees and the ramp is frictionless.

00:10 The pushing force is horizontal and the distance traveled is 2 .5.

00:14 It started initially at rest and the mass of the block is 18 kilograms.

00:19 We are to determine or show the following, the fbd of the box and several work here and a final speed.

00:28 So our main equation that we'll be using will be the definition of work, which is the product of the applied force times the magnitude of the displacement, times the cosine of the angle between the two vectors, which are the applied force and the displacement.

00:46 Another way if looking at work would be the product of the force that is parallel to the displacement or antiparralel or the component of the applied force that is along the axis where the displacement is.

00:59 Also lying.

01:01 Okay.

01:02 Let's start with the first one.

01:04 It will be easier if we also align the x axis along the ramp.

01:09 So, okay, this would be, let me use the black one.

01:15 So this is, oops, this is the x axis.

01:21 Okay.

01:22 And then this is the y.

01:24 This is positive y.

01:26 Going up is positive x.

01:27 And we represent the block as a particle here at the origin.

01:32 Okay, so the most obvious force would be the horizontal pushing force.

01:38 Okay, this is f subp.

01:42 And if this is theta, so this must also be theta.

01:46 Therefore, its x component is going upward.

01:50 This is f px, and the y component is going along negative y.

01:57 So this is f -p -y.

02:00 Okay.

02:01 Now the ramp also applies normal force here.

02:05 So the normal force is called as such because it is normal or perpendicular to the surface that exerts it.

02:12 And then the ever -present force would be the gravitational force that is exerted by the earth on this mass of block.

02:20 And this is also angle theta, angle between the y -axis and the vertical gravitational force.

02:27 Therefore, the weight has two components.

02:31 It has fgy towards negative y and the fgx component that is going downwards or towards negative x.

02:43 Okay.

02:45 So this is now the free body diagram.

02:47 Let's go to the requirement.

02:49 What is the work done by the pushing force? okay.

02:55 Okay, let's use this definition.

02:57 Of work.

03:00 This would be the pushing force fp times the distance traveled times the cosine of the angle between them.

03:09 Okay, let's sketch the two vectors again, tail to tail.

03:15 Displacement is going in this direction.

03:18 And then the pushing force is horizontal...

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