Question

A ball tied to a string of length 0.507 m makes 2.2 revolutions every second. Calculate the speed of the ball. Your answer must be within ± 2.0%

Answer 1

Answer:

The speed of the ball is 6.99 ± 0.14 m/s.

Step-by-step explanation:

The speed of the ball can be calculated using the formula:

v = 2πrf

where v is the speed, r is the length of the string, and f is the frequency of revolutions per second.

In this case, r = 0.507 m and f = 2.2 revolutions per second.

So,

v = 2π(0.507 m)(2.2 rev/s)

v = 6.99 m/s

To find the acceptable range for the answer within ±2.0%, we can use the formula:

acceptable range = ± (2.0/100) × calculated value

So, the acceptable range for the speed is:

acceptable range = ± (2.0/100) × 6.99 m/s

acceptable range = ± 0.14 m/s

Therefore, the speed of the ball is 6.99 ± 0.14 m/s.

Answer 2

The speed of the ball can be calculated using the formula:

v = 2πr/T

where v is the speed of the ball, r is the length of the string, and T is the period of rotation (time taken for one revolution).

In this case, the length of the string is given as 0.507 m and the ball makes 2.2 revolutions every second. Therefore, the period of rotation (T) can be calculated as:

T = 1/f = 1/(2.2 rev/s) = 0.4545 s/rev

The radius of the circular path can be calculated as the length of the string. Therefore,

r = 0.507 m

Substituting these values in the formula, we get:

v = 2πr/T = 2π(0.507 m)/(0.4545 s/rev) = 7.01 m/s

To find the acceptable range of values, we can use the formula for percentage error:

% error = |(actual value - expected value) / expected value| x 100%

Substituting the actual value of v (7.01 m/s) and the expected value (which we can assume to be the nearest integer value, 7 m/s), we get:

% error = |(7.01 m/s - 7 m/s) / 7 m/s| x 100% = 0.14%

Therefore, the answer for the speed of the ball is 7.01 m/s, and it is within ±2.0% of the expected value.