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3 years ago

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

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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3 years ago

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

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3 years ago

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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

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3 years ago