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Alchen [17]
3 years ago
13

A 5 kg block is sliding on a horizontal surface while being pulled by a child using a rope attached to the center of the block.

The rope exerts a constant force of 28.2 N at an angle of \theta=θ = 30 degrees above the horizontal on the block. Friction exists between the block and supporting surface (with \mu_s=\:μ s = 0.25 and \mu_k=\:μ k = 0.12 ). What is the horizontal acceleration of the block?
Physics
1 answer:
aleksandrvk [35]3 years ago
7 0

Answer:

The horizontal acceleration of the block is 4.05 m/s².

Explanation:

The horizontal acceleration can be found as follows:

F = m \cdot a

Fcos(\theta) - \mu_{k}N = m\cdot a

Fcos(\theta) - \mu_{k}[mg - Fsen(\theta)] = m\cdot a  

a = \frac{Fcos(\theta) - \mu_{k}[mg - Fsen(\theta)]}{m}

Where:

a: is the acceleration

F: is the force exerted by the rope = 28.2 N

θ: is the angle = 30°

\mu_{k}: is the kinetic coefficient = 0.12

m: is the mass = 5 kg

g: is the gravity = 9.81 m/s²

a = \frac{28.2 N*cos(30) - 0.12[5 kg*9.81 m/s^{2} - 28.2 N*sen(30)]}{5 kg} = 4.05 m/s^{2}

Therefore, the horizontal acceleration of the block is 4.05 m/s².

I hope it helps you!

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Answer:

The magnitude of the resultant vector is 22.66 cm and it has a direction of 29.33°

Explanation:

To find the resultant vector, you first calculate x and y components of the two vectors M and N. The components of the vectors are calculated by using cos and sin function.

For M vector you obtain:

M=M_x\hat{i}+M_y\hat{j}\\\\M=15.0cm\ cos(20\°)\hat{i}+15.0cm\ sin(20\°)\hat{j}\\\\M=14.09cm\ \hat{i}+5.13\ \hat{j}

For N vector:

N=N_x\hat{i}+N_y\hat{j}\\\\N=8.0cm\ cos(40\°)\hat{i}+8.0cm\ sin(40\°)\hat{j}\\\\N=6.12cm\ \hat{i}+5.142\ \hat{j}

The resultant vector is the sum of the components of M and N:

F=(M_x+N_x)\hat{i}+(M_y+N_y)\hat{j}\\\\F=(14.09+6.12)cm\ \hat{i}+(5.13+5.142)cm\ \hat{j}\\\\F=20.21cm\ \hat{i}+10.27cm\ \hat{j}

The magnitude of the resultant vector is:

|F|=\sqrt{(20.21)^2+(10.27)^2}cm=22.66cm

And the direction of the vector is:

\theta=tan^{-1}(\frac{10.27}{20.21})=29.93\°

hence, the magnitude of the resultant vector is 22.66 cm and it has a direction of 29.33°

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The angular frequency of the wave is determined as 75.4 rad/s.

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A wave function is a mathematical equation for the motion of the wave.

y(x, t) = A sin(kx + ωt + Φ)

where;

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<h3>What is angular frequency?</h3>

The angular frequency is the angular displacement of any wave element per unit of time or the rate of change of the waveform phase.

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ω = 75.4 rad/s

Thus, the angular frequency of the wave is determined as 75.4 rad/s.

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A tall tube is evacuated and its stopcock is closed. The open end of the tube is immersed in a container of water (density 10^3
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Answer:

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Water will rise to equalize the pressure inside and outside the tube.

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p=\rho gh

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ρ = Density of water = 10³ kg/m³

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