Answer :
The length of the cables supporting the trapeze, calculated using the formula for the period of a simple pendulum, is approximately 3.55 meters.
The question involves calculating the length of the cables supporting a trapeze, where the trapeze artist performs with a motion that can be approximated as simple harmonic motion. The given period of the motion is 3.8 seconds, and the acceleration due to gravity (g) is 9.81 m/s2.
To find the length of the cables (L), we use the formula for the period (T) of a simple pendulum, which is a good approximation for our scenario since the swinging motion of a trapeze can be likened to that of a pendulum. The formula is:
T = 2π√(L/g)
Rearranging this formula to solve for L, we obtain:
L = (T2× g) / (4π2)
Substituting the given values:
L = ((3.8)2 × 9.81) / (4π2)
L = 3.55 meters
Therefore, the length of the cables supporting the trapeze is approximately 3.55 meters.
As we know that time period of simple pendulum is given as
T = 2π √L/g
here we know that
T = 3.8 s
now from above equation we know that
T² = 4π² (L/g)
now on rearranging the above equation we will have
L = gT² / 4π²
now plug in all data into it
L = (9.8) (3.8)² / (4) (3.14)²
so the length of the cable must be 3.6 m
T = 2π √L/g
here we know that
T = 3.8 s
now from above equation we know that
T² = 4π² (L/g)
now on rearranging the above equation we will have
L = gT² / 4π²
now plug in all data into it
L = (9.8) (3.8)² / (4) (3.14)²
so the length of the cable must be 3.6 m
