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Firlakuza [10]
3 years ago
10

A slide inclined at 35 takes bathers into a swimming pool. with water sprayed on the slide the bathers spends only one third as

much timeo n the slide as whne its dry. find the coefficient of friction on the dry slide

Physics
1 answer:
Elina [12.6K]3 years ago
6 0
Refer to the figure shown below.

mg =  the weight of the person on the slide.
N = mg cos(35°) = 0.8192 mg, the normal reaction
F = mg sin(35°) = 0.5736 mg, the force acting down the slide.
R = μN = 0.8192 μmg, the resisting force due to friction
μ = the coefficient of dynamic friction on the dry slide.
d =  the length of the slide.
g = 9.8 m/s²
All measurements are in SI units.

We shall consider two cases.

Case 1 (The slide is lubricated by water spray).
Assume that the coefficient of friction is approximately zero.
Let a = the acceleration down the slide. Then
0.5736 mg = ma
a = 0.5736g = 5.6213 m/s²

Let t = the time to travel the length of the slide from rest.
d = (1/2)*(5.6213 m/s²)(t s)² = 2.8106t² m     (1)
t² = 0.3558d
t = 0.5965√d s                                             (2)

Case 2 (The slide is dry)
The time to travel down the slide is 3*(0.5965√t) = 1.7895√t s.
Let a = the acceleration. Then
0.5796mg - 0.8192μmg = ma
a = 0.5796g - 0.8192μg = 5.6801 - 8.0282μ  m/s²

The travel doen the slide from rest is given by
d = (1/2)*(5.6801 - 8.0282μ)*(1.7895√t)²
d = (9.0947 - 12.8544μ)t²                           (3)

Equate (1) and (3).
9.0947 - 12.8544μ = 2.8106
12.8544μ = 6.2841
μ = 0.489

Answer:  μ = 0.49  (nearest hundredth)

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irinina [24]

Answer:

a) 0.275 m b) 13.6 J

Explanation:

In absence of friction, the energy is exchanged between the spring (potential energy) and the cookie (kinetic energy), so at any point, the sum of both energies must be the same:

E = ½ kx2 + ½ mv2

If we take as initial state, the instant when the cookie is passing through the spring’s equilibrium position, all the energy is kinetic, and we know that is equal to 20.0 J.

After sliding to the right, while is being acted on by a friction force, it came momentarily at rest. At this point, the initial kinetic energy, has become potential elastic energy, in part, and in thermal energy also, represented by the work done by the friction force.

So, for this state, we can say the following:

Ki = Uf + Eth = ½* k*d2 + Ff*d

20.0J = ½ *440 N/m* d2 + 11.0 *d, where d is the compressed length of the spring, which is equal to the distance travelled by the cookie before coming momentarily at rest.

We have a quadratic equation, that, after simplifying terms, can be solved as follows, applying the quadratic formula:

d = -0.05/2 +/- √0.090625 = -0.025 +/- 0.3 = 0.275 m (we take the positive root)

b) If we take as our new initial status the moment at which the spring is compressed, and the cookie is at rest, all the energy is potential:

E = Ui = 1/2 k d²

In this case, d is the same value that we got in a), i.e., 0.275 m (as the distance travelled by the cookie after going through the equilibrium point is the same length that the spring have been compressed).

E= 1/2 440 N/m . (0.275)m² = 16.6 J

When the cookie passes again through the equilibrium position, the energy will be in part kinetic, and in part, it will have become thermal energy again.

So, we can write the following equation:

Kf = Ui - Ff.d = 16.6 J - 11.0 (0.275) m = 16.6 J - 3.03 J = 13.6 J

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2 years ago
The graph to the right shows the change in Canada‘s harvest of Atlantic cod from 1950-2004 what year shows the clearest evidence
Ann [662]

The correct answer is C. 1995

Explanation:

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2 years ago
The figure shows three displacement vectors, which are
aleksley [76]

Answer:

the correct answer is D

Explanation:

In this exercise, the vectors are in the same west-east direction, so we can assume that the positive direction is east and perform the algebraic sum.

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where

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       ε = 7.0 m

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the correct answer is D

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