Suppose a 78 kg person is bouncing on a bathroom scale which has a force constant of 1.5 × 106 n/m. 50% part (a) what is the maximum velocity of the person, in meters per second, if the amplitude of the bounce is 0.115 cm?

m = mass of the person bouncing = 78 kg

k = spring constant of the bathroom scale = 1.5 x 10⁶ N/m

v = maximum velocity of the person

A = maximum compression of the spring of scale = 0.115 cm = 0.00115 m

h = height gained at maximum speed = A = 0.00115 m

Using conservation of energy

spring potential energy = kinetic energy + gravitational potential energy

(0.5) k A² = (0.5) m v² + m g h

k A² = m v² + 2 m g h

(1.5 x 10⁶) (0.00115)² = (78) v² + 2 (78) (9.8) (0.00115)

v = 0.0538 m/s

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.