A 3.5-kg box is sliding along a frictionless horizontal surface with a speed of

Question

A 3.5-kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring.
(a) Determine the force constant of the spring, if the box compresses the spring 6.3 cm before coming to rest.

(b) Determine the initial speed the box would need in order to compress the spring by 1.6 cm.

_______________________________________...
A 70-kg rollerblader skates across a skating rink floor. The graph below shows the net external force component F cos along the displacement as a function of the magnitude of the displacement d. Determine the following.
Diagram- http://www.webassign.net/waplots/5/6/cc1e7d17a8c05958b8cb8784ffc156.gif

(a) work done by the net force component F cos acting on the rollerblader as he moves from 0 to 5.0 m

(b) work done by the net force component F cos acting on the rollerblader from 5.0 m to 10.0 m

Thank you in advance for all help, any and all will be greatly appreciated!

Explanation / Answer

here,

mass , m = 3.5 kg

v = 1.8 m/s

a)

compression in the spring , x = 0.063 m

let the spring constant be k

using conservation of energy

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

k * 0.063^2 = 3.5 * 1.8^2

k = 2857 N/m

the spring cosntant is 2857 N/m

b)

let the initial speed be u

when x = 0.016 m

using conservation of energy

0.5 * k * x^2 = 0.5 * m * u^2

2857 * 0.016^2 = 3.5 * u^2

u = 0.46 m/s

the initial speed of the box is 0.46 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.