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lozanna [386]
3 years ago
6

A ball is thrown upward with an initial velocity of 12.1 m/s. How long will it take to reach a velocity of -24.5 m/s?

Physics
1 answer:
Rainbow [258]3 years ago
5 0
<h3><u>Answer;</u></h3>

 = 3.73 seconds

<h3><u>Explanation;</u></h3>

Using the equation;

v = u + at

where v is the final velocity, u is the initial velocity and a is the acceleration due to gravity (-g) and t is the time taken.

Therefore;

v = u - gt

Thus;

v = 24.5 m/s, u = 12.1 m/s, a = -g = 9.8 m/s²

-24.5 m/s = 12.1 - 9.8 × t

36.6 = 9.8 t

t = 36.6/9.8

 = 3.73 seconds

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Answer:

a) F=\frac{\mu_{k}mg}{cos \theta-\mu_{k}sin \theta}

b) \mu_{s}=\frac{Fcos \theta}{Fsin \theta +mg}

Explanation:

In order to solve this problem we must first do a drawing of the situation and a free body diagram. (Check attached picture).

After a close look at the diagram and the problem we can see that the crate will have a constant velocity. This means there will be no acceleration to the crate so the sum of the forces must be equal to zero according to Newton's third law. So we can build a sum of forces in both x and y-direction. Let's start with the analysis of the forces in the y-direction:

\Sigma F_{y}=0

We can see there are three forces acting in the y-direction, the weight of the crate, the normal force and the force in the y-direction, so our sum of forces is:

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F_{y}=Fsin \theta

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N=F sin θ +mg

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so we can find the kinetic friction by substituting for N, so we get:

f_{k}=\mu_{k}(F sin \theta +mg)

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\Sigma F_{x}=0

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-\mu_{k}(F sin \theta +mg)+Fcos \theta=0

so now we can solve for the force, we start by distributing \mu_{k} so we get:

-\mu_{k}F sin \theta -\mu_{k}mg)+Fcos \theta=0

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f_{s}=\mu_{s}(F sin \theta +mg)

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F cos θ = f

when substituting one into the other we get:

F cos \theta=\mu_{s}(F sin \theta +mg)

which can be solved for the static friction coefficient so we get:

\mu_{s}=\frac{Fcos \theta}{Fsin \theta +mg}

which is the answer to part b.

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