21. Fig. 4.1 shows part of a fairground ride with a carriage on ralls.
3.9 m
30°
Fig. 4.1
The carriage of mass 500 kg is travelling towards a slope inclined at 30° to the horizontal.
The carriage has a kinetic energy of 25 kJ at the bottom of the slope. The carriage comes to
rest after travelling up the slope to a vertical height of 3.9 m.
a) Show that the potential energy gained by the carriage is 19 kJ.
g=9.8

b) Calculate the work done against the resistive forces as the carriage moves up the slope.
work done = ...​

The velocity of a car traveling in a straight line increases from 0 meters/second to 30meters/second in 8 seconds. what is the average acceleration of the car?

Six pendulums of mass mand length las shown are released from rest at the same angle theta from vertical. rank the pendulums according to the numberof complete cycles of motion each pendulum goes through perminute. a. l= 1m m=2kg b. l= 4m m=1 kg c. l= 2 m m= 2 kg d. l= 1 m m= 4 kg e. l= 2 m m = 4 kg f. l= 4m m = 4kg

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.