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mars1129 [50]
2 years ago
12

If the applied force is 60 N and the lower mass is 1.0 kg, what is the tension in the string?(frictionless surface)

Physics
1 answer:
Alik [6]2 years ago
3 0

The net force on the larger mass in the horizontal direction (where we take the direction of F to be positive) is

F - T = 2Ma

where T is the magnitude of tension and a is the mass's acceleration.

The net force on the smaller mass in the vertical direction (upward is positive) is

T - Mg = Ma

If M = 1.0 kg and F = 60 N, then we end up with two equations with two unknowns,

60 N - T = (2.0 kg) a

T - (1.0 kg) (9.8 m/s²) = (1.0 kg) a

Eliminate a and solve for T :

(60 N - T) - 2 (T - (1.0 kg) (9.8 m/s²)) = (2.0 kg) a - 2 (1.0 kg) a

60 N - T - 2T + 19.6 N = (2.0 kg) a - (2.0 kg) a

40.4 N - 3T = 0

3T = 40.4 N

T = (40.4 N) / 3

T ≈ 13 N

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Answer:

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Part b)

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Part c)

dT = - \frac{2\pi r}{v^2} dv

Explanation:

Part a)

As we know that force on the passenger while moving in circle is given as

F = \frac{mv^2}{r}

now variation in force is given as

dF = -\frac{mv^2}{r^2} dr

here speed is constant

Part b)

Now if the variation in force is required such that r is constant then we will have

F = \frac{mv^2}{r}

so we have

dF = \frac{2mvdv}{r}

Part c)

As we know that time period of the circular motion is given as

T = \frac{2\pi r}{v}

so here if radius is constant then variation in time period is given as

dT = - \frac{2\pi r}{v^2} dv

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When an airplane flies from Dallas - Ft. Worth International airport to Los Angeles International airport, the time in the air i
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At the intersection of Texas Avenue and University Drive,
Zielflug [23.3K]

Answer:

  • The initial speed of the truck is 21.93 m/s, and the initial speed of the car is 19.524 m/s  

Explanation:

We can use conservation of momentum to find the initial velocities.

Taking the unit vector \hat{i} pointing north and \hat{j} pointing east, the final velocity will be

\vec{V}_f = 16.0 \frac{m}{s} \ ( \ cos(24.0 \°) \ , \ sin (24.0 \°) \ )

\vec{V}_f = ( \ 14.617 \frac{m}{s} \ , \ 6.508 \frac{m}{s} \ )

The final linear momentum will be:

\vec{P}_f = (m_{car}+ m_{truck}) * V_f

\vec{P}_f = (950 \ kg \ + 1900 \ kg \ ) *  ( \ 14.617 \frac{m}{s} \ , \ 6.508 \frac{m}{s} \ )

\vec{P}_f = (2.850 \ kg \ ) *  ( \ 14.617 \frac{m}{s} \ , \ 6.508 \frac{m}{s} \ )

\vec{P}_f = ( \ 41,658.45 \frac{ kg \ m}{s} \ , \ 18,547.8 \frac{kg \ m}{s} \ )

As there are not external forces, the total linear momentum must be constant.

So:

\vec{P}_0= \vec{P}_f

As initially the car is travelling east, and the truck is travelling north, the initial linear momentum must be

\vec{P}_0= ( m_{truck} * v_{truck}, m_{car}* v_{car} ) 

so:

 \vec{P}_0= \vec{P}_f 

( m_{truck} * v_{truck}, m_{car}* v_{car} ) = ( \ 41,658.45 \frac{ kg \ m}{s} \ , \ 18,547.8 \frac{kg \ m}{s} \ )  

so

\left \{ {{m_{truck} \ v_{truck} = 41,658.45 \frac{ kg \ m}{s}  } \atop {m_{car} \ v_{car}=18,547.8 \frac{kg \ m}{s} }} \right.

So, for the truck

m_{truck} \ v_{truck} = 41,658.45 \frac{ kg \ m}{s}

1900 \ kg \ v_{truck} = 41,658.45 \frac{ kg \ m}{s}

v_{truck} = \frac{41,658.45 \frac{ kg \ m}{s}}{1900 \ kg}

v_{truck} = \frac{41,658.45 \frac{ kg \ m}{s}}{1900 \ kg}

v_{truck} = 21.93 \frac{m}{s}

And, for the car

950 \ kg \ v_{car}=18,547.8 \frac{kg \ m}{s}

v_{car}=\frac{18,547.8 \frac{kg \ m}{s}}{950 \ kg}

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Answer:

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Explanation:

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