A power source is going to shake a string and create waves 5.0 cm in amplitude. The string has a linear mass density of 4.0x10-2 kg/m and is pulled under a tension of 100 N. The source can deliver a maximum power of 300 W. What is the highest frequency f at which the source can shake without exceeding the maximum power?

55.13 Hz

Explanation:

Given that :

Amplitude, A =. 5cm = 0.05m

Density, d = 4 * 10^-2

Tension, T = 100N

Power = 300 W

Recall:

Power = 0.5dA²w²v

v = velocity = √T/d ; w = Angular velocity = 2πf

Rewriting our equation :

P = 0.5 * d * A² * (2πf)² * √T/d

300 = 0.5 *(4*10^-2)* 0.05² * 4π² * f² * sqrt(100/0.04)

300 = 0.5*(4*10^-2) * 0.05² * 4π² * f² * sqrt(2500)

300 = 0.02 * 50 * 0.05² * 39.478417 * f²

300 = 0.0986960 * 0.05² * f²

f² = 300 / 0.0986960

f² = 3039.6355

f = sqrt(189.97722)

f = 55.132889

= 55.13 Hz

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.