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Vectors and Forces

Could someone please give me some hints on how to tackle this question, as I'm totally stuck.

1. A book of mass 2.0kg is at rest on a rough tabletop whic is inclined at x degrees to the horizontal.

(a) Draw a vector polygon of the forces acting on the book. (Would the forces be friction and gravity)?

(b) Calculate the angle at which the book initially slips.

(c) Calculate the value of the normal reaction of the tabletop on the book at this angle.

(d) Calculate the resultant force on the book if the tabletop is tilted an additional 10º, assuming the maximum frictional force acts.

Any help would be really appreciated.

Thank you.

Cathy

Reply 1

phys981

10

don't forget the normal reaction force

Reply 2

CathyLou

OP

2

rsk

don't forget the normal reaction force

Would you please be able to show me where all three forces go on the diagram?

Thank you.

Cathy

Reply 3

henryt

17

There will be a force up the slope (parallel to slope), which will be the friction, since friction always opposes the motion of the object, and the book is sliding down the slope. Perpendicular to the slope, there will be a force upwards (normal reaction) and there will be the Weight of the object straight down (regardless of the angle of the slope). Hopefully that should help you with part a).

Reply 4

Gregorian IV

8

CathyLou

Could someone please give me some hints on how to tackle this question, as I'm totally stuck.

1. A book of mass 2.0kg is at rest on a rough tabletop whic is inclined at x degrees to the horizontal.

(a) Draw a vector polygon of the forces acting on the book. (Would the forces be friction and gravity)?

(b) Calculate the angle at which the book initially slips.

(c) Calculate the value of the normal reaction of the tabletop on the book at this angle.

(d) Calculate the resultant force on the book if the tabletop is tilted an additional 10º, assuming the maximum frictional force acts.

Any help would be really appreciated.

Thank you.

Cathy

a. cant draw it on here so won't

b. I think u need to know the frictional force for this. If you do know it then this next bit is helpful. The forward force that makes the book move down the slope is equal to (Weight x sine (angle of the slope).

c. the reaction force is eqaul to weight x cos of the angle of the slop

d. then add on another 10 degrees to the W sin theta value to give the new forward force - add to the frictional force value (i presume its negative) to give a new resultant force

Reply 5

CathyLou

OP

2

Thanks so much both of you for all your help.

Cathy

Reply 6

CathyLou

OP

2

I'm also pretty stuck on this question so I'd really appreciate it if someone could offer some hints.

8. A ship is pulled at a constant speed, v, of 2.5m/s by two tugs, A and B. Each tug is connected to the ship by a cable so that the angle each of the cables makes with the direction of travel is 41 degrees. The ship experiences a drag force given by:

Drag Force (N) = 8000 x velocity^2

(a) Calculate the tension in each cable while travelling at this constant speed. (For this question I got an answer of 66200N in each tug, but I'm not sure if this is correct).

(b) As the tugs attempt to increase the speed of the ship from 2.5m/s, tug A breaks down, with its cable to the ship becoming slack.

<i> Calculate the speed to which the ship initially decelerates, assuming the tension in the other cable remains constant. (Go backwards and work out v through friction force).

<ii> The ship also veers off-course. Explain why this happens.

(c) The harbour authorities want to move the ship to clear the harbour walls sooner. This requires that the tugs increase the tensions in the cables to the ship. The maximum safe tension in the cables is 50kN and the tugs need to maintain a minimum angle of 60 degrees between the cables connecting them to the ship. Calculate the maximum speed at which the tugs can pull the ship.

Thank you.

Cathy

Reply 7

phys981

10

Cathy, for part (a) I get roughly half that for each tug - ie you answer would be the sum of the two.

The friction force is 8000 v^2 and each tug contributes T cos 41 to the forward pull. So 2T cos 41 = 50000.

MY answer isn't EXACTLY half yours but that may be just because we've rounded at different points.

Reply 8

CathyLou

OP

2

Thanks for your help. I thought that my working out was wrong anyway. This is what I did:

Drag force = 8000 x 2.5^2

Drag force = 50000N

Using trigonometry: cos 41º = 50000 / h

0.755h = 50000

h = 66200 N

Tension in Tug A = 66200 N

The tension in Tug B will also be 66200 N as the calculation will be the same.

Cathy

Reply 9

CathyLou

OP

2

Do you have any idea how I could do part b? I really can't get my head around it so I'd be really grateful for any hints.

Thank you.

Cathy

Reply 10

phys981

10

For part B. I assume that the tension stays the same, ie 33100 or whatever it was, in the remaining rope.

So, when it settles at a new constant speed. this will exactly balance the drag force.

So put 8000 v^2 = 33100 and calculate a new value for v

I guess it veers off course because once the other rope breaks, the forces are no longer balanced perpendicular to the directin of travel - ie it's being pulled to one sde because the rope at the other side has broken.

Reply 11

CathyLou

OP

2

Thank you soooo much! That's really helped!

Cathy

Reply 12

rachxl

11

CathyLou

Could someone please give me some hints on how to tackle this question, as I'm totally stuck.

1. A book of mass 2.0kg is at rest on a rough tabletop whic is inclined at x degrees to the horizontal.

(a) Draw a vector polygon of the forces acting on the book. (Would the forces be friction and gravity)?

(b) Calculate the angle at which the book initially slips.

(c) Calculate the value of the normal reaction of the tabletop on the book at this angle.

(d) Calculate the resultant force on the book if the tabletop is tilted an additional 10º, assuming the maximum frictional force acts.

Any help would be really appreciated.

Thank you.

Cathy

I'm sorry to bring this thread up again, but I'm stuck on an identical question! :smile:

part b.... I don't know where to start! Maximum frictional force between the tabletop and the book is 10N. If the angle of the tables inclination is increased the book will slip. At which angle does this initially occur?

If someone could talk me through this I would be very grateful!!

Reply 13

Ash25364731

1

Does anyone know how to do Part C of the ship question?

Original post by Ash25364731

Does anyone know how to do Part C of the ship question?

Hi, welcome to TSR. :smile:

This thread is more than a decade old. It would be better that you start a new thread your own by following the guidlines. Soon this thread would be locked. Thanks.

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