Question

At an outdoor market, a bunch of bananas attached to the bottom of a vertical spring of force constant 16.0 N/m is set into oscillatory motion with an amplitude of 20.0 cm. It is observed that the maximum speed of the bunch of bananas is 35.4 cm/s. What is the weight of the bananas in newtons?

Answer 1

Take amplitude = A = 20.0 cm = 0.2 m
Spring constant = k = 16.0 N/m

Maximum speed = v =35.4 cm/s = 0.354 m/s

Energy's conservation:

(1/2) k A^2 = (1/2) m V^2

So : m = k (A/V)^2 = 16 (0.20/0.354)^2 =5.10Kg

and m g = 5.10*9.81 = 50.03N

Answer 2

1st know these,

Here role of maximum velocity and amplitude is to find out acceleration and with accn we could find mass.

Amplitude = 20cm =0.2 metre

Velocity = 38.2 cm/s = 0.382cm/s

Now

Newtons 3nd law of motion used

V^2 = u^2 +2as

(38.2/100)^2 = 0 + 2a (0.2)

Thus
Acn = (0.382)^2/(0.2*2)

Acn= 0.146/0.4= 0.365m/s2

Now, formula for Simple harmonic motion

Mass* [d^2(x)]/[dt^2] = -k(x)

Where d2x/dt2 = accn at position x

We put x = 0.2meter

Thus

Mass = 16*0.2/0.365 = 8.767 kg

Answer 3

Problem based on "Conservation of Energy" Principle and some understanding.

Take amplitude = A = 20.0 cm = 0.2 m
Spring constant = k = 16.0 N/m
Maximum speed = v = 35.4 cm/s = 0.354 m/s

Maximum Kinetic Energy = Maximum Spring Energy
1/2 Mv

Answer 4

Here role of maximum velocity and amplitude is to find out acceleration and with accn we could find mass.

Amplitude = 20cm =0.2 metre

Velocity = 35.4 cm/s = 0.354cm/s

Now

Newtons 3nd law of motion used

V^2 = u^2 +2as

(35.4/100)^2 = 0 + 2a (0.2)

Thus
Acn = (0.354)^2/(0.2*2)

Acn= 0.313m/s2

Now, formula for Simple harmonic motion

Mass* [d^2(x)]/[dt^2] = -k(x)

Where d2x/dt2 = accn at position x

We put x = 0.2meter

Thus

Mass = 16*0.2/0.313 = 10.214 kg

Answer 5

amplitude (A)=20cm= 0,2m

k=16.0 N/m

V(max) = 0.354 m/s

here,

Potential Energy(max) = Kinetic Energy (max)

0.5 m v^2 = 0.5 k* A ^2

m= 16*0.2*0.2/(0.354^2)

mass of bananas= 5.10 kg

weight of banana = 5.10*9.8=50.04 N

Answer 6

Vmax = A x w

=>35.4 = 20 x w

=> w = 35.4/20 = 1.77 rad/s

=>sqrt(k/m)=1.77

=>m= k/(1.77^2)

=16/(1.77^2)

= 5.11 kg

=> W = mg = 5.11 x 9.8 =50.078 N