What is the mass of an object in the pan if the spring is stretched to a length of 65 cm. (use description to answer).

Question

Hooke's law states that the length that a spring is stretched is proportional to the applied force. A pan hangs from a 50 cm spring. When a 10 kg mass is placed in the pan, it stretches the spring 6 cm.

Answer 1

Hookes law : F = -kx

Suppose mass of the pan is p kg.

When there is nothing in the pan, net force on pan is zero. Force upwards due to spring = -kx = -k x 0.5

Force downwards = pg

So pg -0.5k = 0, so k = 2pg

When we have added 10kg, mass is p+10

Net force is zero, and x = 0.56

So (10+p)g - k (0.56) = 0. k = 2pg

(10+p)g = 0.56 x 2pg

10 + p = 0.56 x 2 p

10 + p = 1,12 p

p = (10 / 0.12) kg

If length of spring is 65 cm, and mass in pan is m kg then

(p+m) g = k (0.65)

k = 2pg

(p+m) g = 0.65 x 2pg

(p+m) = 1.3p

m = 0.3p = 0.3 x (10 / 0.12) kg

Answer 2

Hookes law states that a force is required to stretch or compress a string and the formula for that is F = -kx

F is the force, k is the constant of the spring and x is the elongation of the spring.

According to Newton's second law of motion the acceleration of an object is dependent on two variables. These two variables are net force acting on the object and the mass of said object.

The formula for Newton's law of motion is F = mg which is mass * gravity, so we take this formula and put the MG into Hooke's law to get, ms(g) = -kx.

So now we compute for x and that get's us -x = ms(g)/k, and this is our rule.

I cannot give ya the answer, but if a 10 kg mass is placed in the pan, and it stretches it to 6 cm from a rest of 50 cm then ya just have to plug in the variables. 10kg * 9.8 as the constant for gravity, divided by k will get you -x and the k is the spring force constant and the x is the spring displacement which is 6