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Bond [772]
3 years ago
10

A ball of mass M is suspended by a thin string (of negligible mass) from the ceiling of an elevator.uploaded image

Physics
1 answer:
lilavasa [31]3 years ago
6 0

Answer:

(a) The elevator is traveling upward and its upward velocity is decreasing as it nears a stop at a higher floor.  T > mg

(b) The elevator is traveling upward and its upward velocity is increasing as it begins its journey towards a higher floor. T > mg

(c) The elevator is traveling downward and its downward velocity is decreasing as it nears a stop at a lower floor. T < mg

(d) The elevator is traveling downward at a constant velocity. T = mg

(e) The elevator is traveling downward and its downward velocity is increasing. T < mg

(f) The elevator is stationary and remains at rest. T = mg

Explanation:

To answer this question, consider all the forces acting on the elevator.

The mass of the ball acting downwards due to gravity = mg

The tension on the string depends on upward or downwards force on the ball. T = m(a+g)

where a is acceleration and increase in velocity causes increase in acceleration, and vice versa. (a = v/t)

(a) The elevator is traveling upward and its upward velocity is decreasing as it nears a stop at a higher floor.

If the upward velocity is decreasing, its acceleration is also decreasing, and acceleration is not equal to Zero

T = m(a+g) > mg

(b) The elevator is traveling upward and its upward velocity is increasing as it begins its journey towards a higher floor.

If the upward velocity is increasing, its acceleration is also increasing.

Then, T = m(a+g) > mg

(c) The elevator is traveling downward and its downward velocity is decreasing as it nears a stop at a lower floor.

If the downward velocity is decreasing, its acceleration is also decreasing, and acceleration is not equal to Zero

T = m(a-g) < mg

(d) The elevator is traveling downward at a constant velocity

At constant velocity, acceleration is zero, because acceleration is the rate of change of velocity.

T = m(0+g) = mg

(e) The elevator is traveling downward and its downward velocity is increasing

If the downward velocity is increasing, its acceleration is also increasing

T = m(a-g) < mg

(f) The elevator is stationary and remains at rest.

if the elevator is at rest, its acceleration is zero

T = m(0+g) = mg

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A person is running at 2 m/s and 20 s later is running at 22 m/s. What is
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Four charges of equal magnitude, q = +1 uC, are placed at the four corners of a square with a side length of 1 meter located in
Anastasy [175]

Answer:

a)     F _total = 15.08 10⁻³ N ,   b)   m = 1,539 10⁻³ kg

Explanation:

a) To solve this problem we can use Coulomb's law to find the force created by each charge

          F =k \frac{\ q_{1} q_{2} }{r_{12}^{2}  }

and the total force is

          F = F₁₅ + F₂₅ + F₃₅ + F₄₅

The bold are vectros, In the exercise they indicate the charges

          q₁ = q₂= q₃ = q₄ =  1 10⁻⁶ C

          q₅ = 2 10⁻⁶ C

Let's set a reference system where the sphere is on the z axis and the other charges on the xy plane, let's write the coordinates of card charge

sphere (subscript 5)

   x₅ = 0

   y₅ = 0

   z₅ = 2 m

charge 1

   x = 0.5 m

   y = 0.5 m

   z = 0

charge 2

   x = -0.5 m

   y = 0.5 m

   z = 0

 

charge 3

   x = -0.5 m

   y = -0.5 m

   z = 0

charge 4

   x = 0.5 m

   y = -0.5 m

   z = 0

With these values ​​we can calculate the distance between each charge and the sphere

charge 1 and sphere

       r₁₅² = (x₅ -x₁)² + (y₅ - y₁)² + (z₅ -z₁)²

substitute

       r₁₅² = (0- 0.5)² + (0 - 0.5)² + (2 -0)²

       r₁₅² = 0.5² + 0.5² + 2²

       r₁₅² = 4.5

we can see that for the other charges the result is the same since being squared always gives positive

      r₁₅ = r₂₅ = r₃₅ = r₄₅

the force created by the card charge on the sphere is the projection on the Z axis of the total force

Let's find the angle with respect to the Z axis

            tan φ = r / z

where r is the magnitude of the vector in the xy plane

          r = \sqrt{0.5^{2} + 0.5^{2} }

          r = 0.7071 m

         φ = tan⁻¹ r / z

         φ = tan⁻¹ (0.7071 / 2)

         φ = 19.5

consequently the total force is

        F_total = 4 F cos 19.5

        F _total =   4 \frac{k \ q_{1}  q_{5}  }{r_{15}^{2}}   cos 19.5

let's calculate

        F_toal = 4 9 10⁹ 1 10⁻⁶ 2 10⁻⁶ /4.5    cos 19.5

        F _total = 15.08 10⁻³ N

b) For this part indicate that the sphere is in equilibrium with the weight

           F_total - W = 0

           W = mg

           F_total = mg

           m = F_total / g

           m = 15.08 10³ / 9.8

           m = 1,539 10⁻³ kg

5 0
3 years ago
A swimmer swims a half lap, moving from the left end to the right end of a pool that is 50 meters long. What is the Distance and
lina2011 [118]
<h2><u>Answer</u>:</h2>

Distance = 50m

Displacement = 50m to the right

<h2><u>Explanation</u>:</h2>

<em>Distance</em> is the total length of a given path. It is a scalar quantity and thus takes no consideration on the direction of the path.

<em>Displacement</em> on the other hand is the change in position of an object. It is a vector quantity and takes consideration on the direction of the object.

From the question:

<em>The swimmer swims half lap by moving from the left end to the right end of a pool that is 50m long.</em>

Distance = total length of the given path = 50m

Displacement = change in position of the swimmer from the left end (0m) to the right end (50m) = 50 - 0 = 50m

Since direction is important in displacement, the complete details of the displacement should be 50m to the right

6 0
3 years ago
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