CP? A 6.50-kg instrument is hanging by a vertical wire inside a spaceship that is blasting off from rest at the earth’s sur-face. This spaceship reaches an altitude of 276 m in 15.0 s with constant acceleration. (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 47P Step 1 of 5: Given data, Mass of the instrument, m = 6.5 kg Distance, s= 276 m Time taken, t= 15 s Vertical component,(Since motion of spaceship is along vertical direction) Initial velocity, u= 0 Acceleration due to gravity, a 1 g = 9.8 m/s 2 Step 2 of 5: (a) Draw a free-body diagram for the instrument during this time. Indicate which force is greater. Above figure shows the FBD for the instrument in spaceship. The tension force is greater than the weight of the instrument as the acceleration of the spaceship is upward as shown in the above figure. Step 3 of 5: (b) ind the force that the wire exerts on the instrument. The net acceleration of the instrument is due to both acceleration due to gravity and the due acceleration of the the spaceship. To calculate the acceleration of the instrument due to motion of space ship, Using kinematics formula, s= ut + a t 2 2 1 1 2 Since u= 0, s= a2t1 solving for acceleration, a1= 22s t Substituting s= 276 m, t= 15 s 2 (276 m) a1= (15 s) a =2.45 m/s 2 1