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Darya [45]
2 years ago
15

The initial speed of a body is 4.24 m/s. What is its speed after 2.91 s if it accelerates uniformly at -1.76 m/s2

Physics
1 answer:
shutvik [7]2 years ago
6 0
  • Initial velocity=u=4.24m/s
  • Time=t=2.91s
  • Acceleration=a=-1.76m/s^2
  • Final velocity=v

Using 1st equation of kinematics

\\ \sf\longmapsto v=u+at

\\ \sf\longmapsto v=4.24+2.91(-1.76)

\\ \sf\longmapsto v=|4.24-5.12|

\\ \sf\longmapsto v=0.8m/s

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Please help me with the formular of this question and the solvings.​
sweet [91]

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\displaystyle T=48.86\ N

Explanation:

<u>Net Force </u>

The second Newton's law explains how to understand the dynamics of a system where several forces are acting. The forces are vectorial magnitudes which means the x and y coordinates must be treated separately. For each component, the net force must equal the mass by the acceleration, i.e.

F_{nx}=ma_x

F_{ny}=ma_y

The box with mass m=20 kg is pulled by a rope with a \theta= 30^o angle above the horizontal. It means that force (called T) has two components:

T_x=Tcos\theta

T_y=Tsin\theta

We'll assume the positive directions are to the right and upwards and that the box is being pulled to the right. There are two forces in the x-axis: The x-component of T (to the right) and the friction force (to the left). So the equilibrium equation for x is

\displaystyle T\ cos\theta -Fr=m.a

There are three forces acting in the y-axis: The component of T (upwards), the weight (downwards), and the Normal (upwards). Since there is no movement in the y-axis, the net force is zero and:

\displaystyle N+T\ sin\theta -mg=0

Rearranging:

\displaystyle N+T\ sin\theta =mg

Solving for N in the y-axis:

\displaystyle N=mg-T\ sin\theta

The friction force is given by

\displaystyle Fr=\mu.N

Replacing in the equation for the x-axis, we have

\displaystyle T\ cos\theta -\mu\ N=ma

Replacing the formula for N in the equation for the x-axis  

\displaystyle T\ cos\theta -\mu(mg-T\ sin\theta)=ma

Operating and rearranging

\displaystyle T\ cos\theta -\mu\ mg+T\ \mu\ sin\theta=ma

\displaystyle T\ (cos\theta +\mu\ sin\theta)=ma +\mu\ mg

Solving for T:

\displaystyle T=\frac{a+\mu\ g}{cos\theta +\mu\ sin\theta }\ m

Plugging in the given values:

\displaystyle T=\frac{0.4+0.2(9.8)}{cos30^o+0.2\ sin30^o }\ .20

\boxed{\displaystyle T=48.86\ N}

7 0
2 years ago
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