Physics question- work and energy?

Question

1) If a car traveling at 58 km/h will skid 22 m when its brakes lock, how far will it skid if it is traveling at 120 km/h when its brakes lock?

2) A certain car can go from 0 to 95 km/h in 7 s. If the engine delivered twice the power to the wheels, how many seconds would it take?

Answer 1

Wow these are some good questions, they made me stop and think for a second about how to actually think about them. For the first one you must remember that work is done to change kinetic energy, in this case the brakes are doing work to slow the car down. Since the brakes are the same in both cases it can be assumed that the average force the car experiences while slowing down is the same in both instances, basically a frictional force between the brake pads and the rotor disks in your wheel. It is our goal to find this force first.

m=mass of car
F = force of the brakes
v1 = 58km/hr. = 16.11m/s
d1 = 22m
v2 = 120 km/hr = 33.33m/s
d2 = ???

change in KE = 1/2 * m * v1^2
W = change in KE = F*d1 = 1/2 *m*v1^2
F = m*v1^2 / (2*d1), the force of the brakes, which is constant so
change in KE2 = F * d2 = m * v1^2 * d2 / (2*d1) = 1/2 *m * v2^2

Mass and the factor of 1/2 cancel out leaving us with

v1^2 *d2/d1 = v2^2 Solve for d2 (it turns out that units of velocity do not matter)

d2 = v2^2 * (d1/v1^2) = (120 km/h)^2*(22m/(58km/h)^2) = 14400/3364*22m = 94 m

So it goes 94 m at the higher velocity

For the second one remember that Power is Work/time. So we want to find the total work done to accelerate this car, can be found by the change in kinetic energy.

1/2*m*(95km/h)^2 = work

This work is done over the course of 7 sec. so the power of the engine is total work divided by 7 seconds.

Power = 1/7*1/2*m*(95km/h)^2

Now we want to find out how fast we can do this amount of work if power is doubled.

New Power = 2*Power = 1/7*m*(95km/h)^2

New Power = Work/New time

1/7*m*(95km/h)^2 = 1/2*m*(95km/h)^2/ t

As can be seen m and the velocity term cancels out and we get

1/7 = 1/(2t) so 7 = 2t ; t =3.5 sec.

So twice the power means half the time (3.5 s)

Hope this helps, email me if you have anymore questions.

Answer 2

once you dropped the water drop into the pool, it converted means means into kinetic means because it fell down. It hit the outdoors of the pool and did right here: one million. Make a noise 2. grant a undeniable volume of means to the pool of water which a. raised the temperature of the pool ever so somewhat b. led to a ripple to ensue and unfolded c. forced a breakage interior the outdoors layer around the drop and on the pool d. threw some water into the air (after the drop hit the outdoors) the sound waves hit your ears, the partitions, even though and have been the two bounced off or absorbed. The air itself absorbed extremely some the sound means, heating it up ever so somewhat. The ripples bounced off the facets of the pond and moved lower back and forth somewhat till the internal viscosity of the water and the outdoors rigidity finally placed sufficient drag on them. additionally any comfortable stuff alongside the facets of the pond absorbed extremely some the means. Now, there is yet another rule (the 2d regulation of thermodynamics) in physics which says that means travels from a severe concentration to a low concentration, and that's exactly what occurred. quite of being concentrated on the drop, it unfolded over all the pond and area and grow to be dissipated. stable question. You controlled to cover 2 needed thermodynamics policies in one shot in an outstanding actually understood difficulty.