A22.5 kg chair attached to a spring takes 1.30 s to complete one cycle of oscillation. with an astronaut sitting in the oscillating chair with feet off the floor, a full oscillation cycle takes 2.54 s. what is the astronaut's mass?

85.689 kg is the astronaut's mass.

Explanation:

Given data: m = 22.5 kg   and T = 1.3 sec

So, using the below formula,

Now, after putting the values of m and T in the above equation, we will find out the value of k which is as,

To remove the square root, take square on both sides, we get,

Now, we have the same string but this time we have different mass and different time. So, let the mass of the astronaut is and = 2.54 sec, k= 525.7 kg. Apply these values in the equation, we get,

Taking squares on both sides, we get,

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.