Question

A block of mass m = 1.7 kg is released from rest at a height of H = 0.93 m on a curved frictionless ramp. At the foot of the ramp is a spring whose spring constant is k = 735.0 N/m. What is the maximum compression of the spring, x?

Answer 1

Answer:

The maximum compression of the spring $x = 0.205$ m

Explanation:

Given :

Mass of block $m =$ 1.7 Kg

Height $h = 0.93$ m

Spring constant  $k = 735 \frac{N}{m}$

From the conservation of energy,

Here, potential energy of the block is converted into elastic potential energy of spring.

  $\frac{1}{2} k x^{2} = mgh$

Where $x =$ maximum compression of the spring,  $g = 9.8 \frac{m}{s^{2} }$  

$\frac{1}{2} \times 735 \times x^{2} = 1.7 \times 9.8 \times 0.93$

   $x^{2} = 0.0423$

    $x = \sqrt{0.0423} = 0.205$ m

Hence, the maximum compression of the spring $x = 0.205$ m