. A rope 2 metres long rests on a table where the coefficient of friction is 0.5. What minimum length of rope can stay on the table before the whole rope will slip off?
a) 133 cm
b) 80 cm
c) 200 cm
d) Cannot determine without more information.
The answer is A but i can't figure out how to do it.
force friction=mu*lengthdensity*L*g
force hanging over=lengthdensity*(2-L)*g
set them equal
mu*L*sigma*g=sigma*(2-L)g
sigma*g(.5L-2+L)=0
1.5L=2
L=4/3 meter or answer a.
length on table = x
length over side = 2-x
mass/meter length = m
mass on table = m x
max friction force =.5 m g x
mass over the side = m(2-x)
weight over the side = m g(2-x)
if slips when
.5 m g x = m g (2-x)
x = 2 (2-x)
3 x = 4
x = 4/3 = 1.33 meter = 133 cm
To determine the minimum length of rope that can stay on the table before the whole rope slips off, we need to consider the forces acting on the rope. The force of friction plays a crucial role in this situation.
Here's how you can solve it step by step:
1. Start by calculating the normal force acting on the rope. The normal force is the force exerted by the table perpendicular to its surface. In this case, it is equal to the weight of the rope.
The weight of the rope can be calculated using the formula: Weight = Mass × Gravity
Since the mass of the rope is not given, we cannot determine it precisely. This means we need additional information to find the weight accurately. Therefore, the answer is (d) Cannot determine without more information.
So, in summary, without the mass or weight of the rope given, it is impossible to determine the minimum length of the rope that can stay on the table before it slips off.