Question

A block of mass 2 kg drops vertically from a height of 0.4 m onto a spring whose force constant k is 1960 N/m. Therefore, the maximum compression of the spring is:

a) 0.02 m
b) 0.04 m
c) 0.06 m
d) 0.08 m

Answer 1

The maximum compression of the spring is approximately 0.089 m, which is closest to option d) 0.08 m.

Step-by-step explanation:

The maximum compression of the spring can be determined using the law of conservation of energy. When the block falls from a height of 0.4 m, it gains potential energy which is then converted into the potential energy stored in the spring when it compresses. The gravitational potential energy gained by the block is given by:

PE = mgh

where m is the mass of the block (2 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (0.4 m). Plugging in the values:

PE = (2 kg)(9.8 m/s^2)(0.4 m) = 7.84 J

The potential energy stored in the spring is given by:

PE = 0.5kx^2

where k is the force constant of the spring (1960 N/m) and x is the maximum compression of the spring. Rearranging the equation:

x = sqrt(2PE/k) = sqrt(2(7.84 J)/(1960 N/m)) = sqrt(0.008 m^2) = 0.089 m

Therefore, the maximum compression of the spring is approximately 0.089 m, which is closest to option d) 0.08 m.