An elevator is ascending at a constant velocity. A block of mass m is suspended

Question

An elevator is ascending at a constant velocity. A block of mass m is suspended from the ceiling of the elevator by a rope, as shown in the figure.

1)   Which of the following is true of the magnitude of the tension T in the rope?

a. T = mg

b. T < mg (but greater than zero)

c. T > mg

d. T = 0

Now assume the elevator is accelerating upward with a constant non-zero acceleration.

2)  Which of the following is true of the magnitude of the tension T in the rope?

a. T = mg

b. T < mg (but greater than zero)

c. T > mg

d. T = 0

Now assume the elevator is accelerating down with a constant non-zero acceleration.

3)  Which of the following is true of the magnitude of the tension T in the rope?

a. T = mg

b. T < mg (but greater than zero)

c. T > mg

d. T = 0

Finally, assume the elevator is in "free-fall" (accelerating down with acceleration -9.8 m/s2).

4)  Which of the following is true of the magnitude of the tension T in the rope?

a. T = mg

b. T < mg (but greater than zero)

c. T > mg

d. T = 0

A ball is swung in a horizontal circle (A view from above is shown below).

8)  If the string is cut at the moment shown, which path will the ball take?

a. A

b. B

c. C

d. D

e. E

Explanation / Answer

(1) At constant velocity, acceleration = 0

So, only weight of the block 'mg' will acts in the downward direction.

So, T = mg

Option (a) is the correct answer.

(2) Accleration is in upward direction.

Suppose 'a' is the acceleration.

In this case, Tension, T = m(a+g)

Means, T > mg

So, option (c) is the correct answer.

(3) In this case, T = m(g-a)

So, option (b) is the correct answer.

(4) Under free-fall condition, T = 0

So, option (d) is the correct answer.

(8) The ball is acted by two forces.

First - directed out from the center

Second - towards the tangential direction of the circle.

The resultant is towards the direction shown by the option B

Hence option (b) is the correct answer.

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