- #1

- 347

- 2

## Homework Statement

A block of mass 100g is at rest on a rough horizontal plane. It has a massless rope attached to one end inclined at 20° above the horizontal. When the tension in the string is 0.5N the object is found to be in limiting equilibrium.

Part A: Find the coeffecient of static friction between the object and the plane.

Part B: What would the tension in the string have to be to make the object accelerate at 1.5m/s^2.

## Homework Equations

Fnet=ma

R=mg (R is the normal reaction force)

## The Attempt at a Solution

For clarification, F_f is the frictional force. and P is the unkown foce in part B.

Part A:

[itex]

0.5cos20=0.47\\

0.5sin20=0.17\\

mg=R+0.17\\

0.98=R+0.17\\

∴ R=0.98-0.17=0.81\\

F_f=0.5cos20 (because \space the \space force \space applied\space by\space the\space string\space to\space the\space horizontal \space must \space equal \space the \space frictional \space force)\\

∴F_f=0.47\\

μR=0.47\\

μ0.81=0.47\\

∴ μ \frac{0.47}{0.81}=0.58 \\

[/itex]

Part B:

[itex]

R+Psin20=mg \\

R+Psin20=0.98 \\

∴ R=0.98-0.34P \\

\\

Pcos20-F_f=ma\\

Pcos20-μR=0.15\\

∴0.94P=0.15+0.58R\\

0.94P=0.15+0.58(0.98-0.34P)\\

0.94P=0.15+0.57-0.2P\\

1.14P=0.15+0.57\\

1.14P=0.72\\

∴ P=\frac{0.72}{1.14}=0.63N \\

[/itex]

My main issue is if I have done it right because the answer to Part B seems rather low compared to the force when it is in limiting equilibrium i.e. only 0.13N more.

Any help/pointers is appreciated.

Last edited: