For fun, you strap roller skates to a washing machine and let it go at the top o

Question

For fun, you strap roller skates to a washing machine and let it go at the top of a ramp. It rolls down the ramp and then along a level walk until it collides with a horizontal spring, which momentarily stops it.

a) Name each force that acts on the washing machine during this interval (from release to momentarily stopping), stating whether it does positive, negative, or zero work on the washing machine.

b) The top of the ramp is between 1.5 m above the sidewalk, the washer's mass is between 60kg, and the spring compresses from 70cm to 30 cm while stopping the washer. Calculate the spring's force constant k, assuming conservation of mechanical energy.

c) Since that was fun, you try again, this time shoving the washing machine from the top of the ramp, instead of simply letting it go. You push it with a force of between 300 N, and you’re able to push it for 3 m along the ramp before losing contact. How far does the spring compress, this time?

Explanation / Answer

a)

while moving on the ramp , forces acting are

normal force by the ramp perpendicular to incline , does no work since normal force is perpendicular to direction of motion of washing machine

weight force in down direction , does positive work

frictional force at the wheels of the roller , does negative work

during motion on level walk :

normal force in Upward direction perpendicular to the surface , does no work since direction of force is perpendicular to direction of motion

weight force in down direction , does no work since direction of force is perpendicular to direction of motion

spring force , does negative work as it acts in opposite direction of the motion

b)

x = compression of spring = 70 - 30 = 40 cm = 0.4 m

using conservation of energy

potential energy of the washer = spring energy

mgh = (0.5) k x2

(60) (9.8) (1.5) = (0.5) k (0.4)2

k = 11025 N/m

c)

using conservation of energy

mgh + Fd = (0.5) k x2

(60) (9.8) (1.5) + (300) 3 = (0.5) (11025) x2

x = 0.57 m

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