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faust18 [17]
3 years ago
5

A cylinder of diameter 100 mm rolls from restdown a 5 m long ramp and its center of mass is moving with velocity 2 m/s at the bo

ttom of the ramp. (a) What is its (constant) acceleration down the ramp? (b) What is its angular acceleration?
Physics
1 answer:
RoseWind [281]3 years ago
3 0

Answer:

(a): a = 0.4m/s²

(b): α = 8 radians/s²

Explanation:

First we propose an equation to determine the linear acceleration and an equation to determine the space traveled in the ramp (5m):

a= (Vf-Vi)/t = (2m/s)/t

a: linear acceleration.

Vf: speed at the end of the ramp.

Vi: speed at the beginning of the ramp (zero).

d= (1/2)×a×t² = 5m

d: distance of the ramp (5m).

We replace the first equation in the second to determine the travel time on the ramp:

d = 5m = (1/2)×( (2m/s)/t)×t² = (1m/s)×t ⇒ t = 5s

And the linear acceleration will be:

a = (2m/s)/5s = 0.4m/s²

Now we determine the perimeter of the cylinder to know the linear distance traveled on the ramp in a revolution:

perimeter = π×diameter = π×0.1m = 0.3142m

To determine the angular acceleration we divide the linear acceleration by the radius of the cylinder:

α = (0.4m/s²)/(0.05m) = 8 radians/s²

α: angular aceleration.

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The coefficient of kinetic friction (μ) between the block and the table is 0.4.

<h3>What is kinetic friction?</h3>

This sis the frictional force between an object in motion with the surface in contact.

μN = ff

where;

  • N is normal reaction due to weight of the block
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μ = ff/N

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Thus, the coefficient of kinetic friction (μ) between the block and the table is 0.4.

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A student pulls horizontally on a block with a spring scale. The block reads 24.5 Newtons before the block starts to move. It re
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Answer:

The coefficient of friction causes the force on the object to be less than its initial reading on the spring scale.

Explanation:

Since the block reads 24.5 N before the block starts to move, this is its weight. Now, when the block starts to move at a constant velocity, it experiences a frictional force which is equal to the force with which the student pulls.

Now, since the velocity is constant so, there is no acceleration and thus, the net force is zero.

Let F = force applied and f = frictional force = μN = μW where μ = coefficient of friction and N = normal force. The normal force also equals the weight of the object W.

Now, since F - f = ma and a = 0 where a = acceleration and m = mass of block,

F - f = m(0) = 0

F - f = 0

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Since the force applied equals the frictional force, we have that

F =  μW and F = 23.7 N and W = 24.5 N

So, 23.7 N = μ(24.5 N)

μ = 23.7 N/24.5 N

μ = 0.97

Since μ = 0.97 < 1, the coefficient of friction causes the force on the object to be less than its initial reading on the spring scale.

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