Question

A 7.30-kg instrument is hanging by a vertical wire inside a space ship that is blasting off at the surface of the earth. This ship starts from rest and reaches an altitude of 276 m in 19.0 s with constant acceleration.Draw a free-body diagram for the instrument during this time.(Assume that the space ship is accelerating upward. )Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

Answer 1

T = 82.78 N

Step-by-step explanation:

Given:

- Initial velocity V_i = 0

- Time taken to reach given altitude t = 19.0 s

- Reach and altitude of y_f = 276

- Initial altitude y(0) = 0

- mass of instrument m = 7.30 kg

Find:

(a) Draw a free-body diagram for the instrument during this time. Indicate which force is greater.

(b) Find the force that the wire exerts on the instrument.

Solution:

a)

Forces: One downwards force due to weight and one upward force due to tension on the instrument:

kinetic: There is one kinetic motion of instrument in upwards direction. Which imparts and extra force in upwards direction i.e F= ma. This increases the tension in the string. The Tension is string is greater that weight of the instrument. Hence, T > W = m*g. See attachment.

b)

Use second equation of motion and compute the acceleration:

y_f = y(0) + V_i*t + 0.5*a*t^2

- Input the values:

276 = 0 + 0 + +0.5*a*(19.0)^2

a = 276*2 / 19.0^2

a = 1.53 m/s^2

- Use Newton's second law of motion in vertical direction:

F_net = m*a

T - m*g = m*a

- Plug in the values:

T - 7.30*9.81 = 7.30*1.53

T = 7.30*(1.53 + 9.81)

- Compute the tension in the string:

T = 82.78 N