1/ A 20.0-kg crate sits at rest at the bottom of a 19.5m -long ramp that is incl

Question

1/ A 20.0-kg crate sits at rest at the bottom of a 19.5m -long ramp that is inclined at 31? above the horizontal. A constant horizontal force of 290 N is applied to the crate to push it up the ramp. While the crate is moving, the ramp exerts a constant frictional force on it that has magnitude 65.0 N.

a) What is the total work done on the crate during its motion from the bottom to the top of the ramp?

b) How much time does it take the crate to travel to the top of the ramp?

2/ Three identical 5.00kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 3.80kN/m and was 19.0cm long before any masses were attached to it. How long is each spring when hanging as shown?
(Hint: First isolate only the bottom mass. Then treat the bottom two masses as a system. Finally, treat all three masses as a system.)(Figure 1) bottom spring, middle spring, and top spring.

3/ The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At full power, the car can accelerate from zero to 32.0mph in time 1.00s .

a) At full power, how long would it take for the car to accelerate from 0 to 64.0mph ? Neglect friction and air resistance.

Explanation / Answer

3/

initail velocity u = 0 m/s

final velocity v = 32 mp/h = 14.30 m/s

a)

at the full power the car accelerate from 0 to 14.30 m/s in 1 sec

so by using

v = u + at

14.30 = 0 + a * 1

a = 14.30 m /s^2

so the time taken by the car to accelerate from 0 to 64 mp/h is

v = 64mp/h = 28.61 m/s

v = u +at

28.61 = 0 + 14.30 * t

t = 2 sec

the time taken by the at full power to accelerate from 0 to 64 mp/h is 2sec

there is no fig. for the 1 and 2 questions

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