must be done to stretch spring an additional 15 cm? Example 5: A 250 N/m spring

Question

must be done to stretch spring an additional 15 cm? Example 5: A 250 N/m spring has an un-stretched length of 8 cm. A force stretches the spring until it is 12 c long. How much work was done by the stretching force? Example 6: A 2.6 kg box rests on a rough (u 0.67) horizontal floor. Find the change in the kinetic energy of the box if a 31.2 N horizontal force pushes the box 12.4 m. (Assume the box starts from rest. Example 7: One end of a 1000 N/m spring is attached to a wall, a 5 kg block is attached to the other end. If the spring is then compressed a maximum of 10 cm, what is the maximum speed of block after the spring is released? (Assume that the block moves on a smooth horizontal surface.) Example 8: climb the rope? (Assume that she climbs at a constant speed Example 9: A 90 ib girl climbs up a 12 ft length of rope. If she can develop 0.1 hp, how long does it take her to A car needs 30 hp in order to travel at a constant 60 mph. What is the frictional force that acts on the car?

Explanation / Answer

Example 5:

work done by stretching force=0.5*spring constant*elongation^2

=0.5*250*(0.12-0.08)^2

=0.2 J

Example 6:

change in kinetic energy=work done by the force - work done against friction

=force*distance-friction force*distance

=force*distance-friction coefficient*normal force*distance

=31.2*12.4-0.67*2.6*9.8*12.4

=175.19 J

Example 7:

potential energy of the spring will be converted to kinetic energy of the block.

let speed be v m/s.

then 0.5*mass*v^2=0.5*spring constant*compression^2

==>5*v^2=1000*0.1^2

==>v=1.4142 m/s

Example 8:

1 hp=745.7 W

1 lb=4.44822 N

1 ft =0.3048 m

power*time=energy=force*distance

==>74.57 W*time=400.34 N*3.6576

==>time=19.636 seconds

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