Question

A 1.5kg crate falls from a height of 2.0 onto an industrial spring scale with a spring constant of 1.5exponent5 n/m . At it's greatest compression the reading on the scale is:
A) 15N
B) 30N
C) 1.5 exponent3 N
D) 3.0 exponent 3 N​

Answer 1

Answer:

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Answer 2

Given: 1.5 kg crate falls from height of 2 m onto an industrial spring scale. The spring constant 1.5* 10^5 N/m

To find: Reading of the scale at its greatest compression

Explanation: Mass(m)= 1 kg

Height(h) = 2 m

Potential energy= mgh

= 1*10*2

= 20 J

When it falls on spring, gravitational potential energy gets converted to spring potential energy. It compresses the spring till all the potential energy gets converted.

Spring constant (k)= 1.5* 10^5

So,

$\frac{1}{2} \times k \times {x}^{2} = 20$

$k {x}^{2} = 40$

${x}^{2} = \frac{20}{1.5 \times {10}^{5} }$

${x}^{2} = 13.3 \times {10}^{ - 5}$

x = 0.012 m

Reading on scale= Force

= kx

= 1.5* 10^5 * 0.012

= 1.52* 10^3 N

Therefore, the reading of the scale ls is option (c) 1.5* 10^3 N.