How are mass and acceleration the same?

Answer 1

Explain why engines withequal power accelerate cars with a small mass quicker than cars with a large mass?

I hope your question is, "Why would the smaller car take less time to accelerate from 0 - 60 mph"?

Power measures the amount of energy provided per second. The energy provided is used to increase the velocity of the car (mass) to a specific velocity, 60mph. Since the change in velocity is the same for both cars, and Kinetic energy= ½ · mass · (velocity) 2, the greater the mass, the more energy needed to increase the velocity of the car to that specific velocity. Since Energy = Power · time, and power is constant, the only way to provide the more energy is to provide that same amount power for a longer period of time. For example, for a 10 kg car to reach a velocity of 5 m/s, requires ½ · 10 · 52 = 125 joules of energy. For a 20 kg car reach a velocity of 5 m/s, would requires ½ · 20 · 52 = 250 joules of energy. The energy is being supplied by a 25 Watt motor, which supplies 25 joules of energy per second. The 10 kg car requires 125 joules ÷ 25 joules per second, which will take 5 seconds. The 20 kg car requires 250 joules ÷ 25 joules per second, which will take 10 seconds.

Kinetic energy = ½ · mass · (velocity) 2, so change in Kinetic energy = ½ · mass · (velocityfinal2 -- velocityinitial2)

If we consider the car is accelerating from 0 - 60mph, velocityinitial = 0 mph, velocityfinal = 60mph

1. Change in Kinetic energy = ½ · mass · (velocityfinal) 2

2. Power = Change in Kinetic energy = ½ · mass · (velocityfinal) 2

time time

3. Power · time = ½ · mass · (velocityfinal) 2

See this web site to see picture and specs for the following car

http://www.leftlanenews.com/bugatti-veyron-16.4.html Bugatti Veyron 16.4 Grand Sport

Curb Weight (lbs) = 4470 lbs. Horsepower = 1001 @ 6000 rpm

Slug is the unit of mass in the English Measurement system, like Kilogram in the metric system.32.2 Slugs = 1 pound, so mass of car = 4470 ÷ 32.2 = 138.8 slugsUse Eq. 6 to determine the time for the car to accelerate from 0 -- 60 mph. 60 mph = 88ft/s

One mechanical horsepower = 550 foot-pounds per second.

4. (Powerfrom Engine) · time = 0.5 · mass · (velocityfinal)2

5. (# of Hp) · 550 ft-lbs/s- Hp · (time ) = 0.5· ( # of slugs) · ( 88 ft/s)2

6. 1000 Hp · 550 ft-lbs./s- Hp· (time ) = (0.5) ·(138.8 slugs) · ( 88 ft/s)2

Timesec = 0.98 seconds

According to the equation, the time to accelerate from 0 to 60 mph = 0.98 sec According to the Car website below, time to accelerate from 0 to 60 mph = 2.6 sec

http://www.leftlanenews.com/bugatti-veyron-16.4.html

The car loses some of the energy as it spins its tires taking off. The 0.98 second time is for a 100% efficient situation. Any heat given off is a loss of energy. At 6000 rpm, the engine, the transmission and other parts of the drive train are getting hot.

Now let, try the same problem for a car of ½ the mass = ½ of 138.8slugs = 69.4 slugs and the same power.

7. 1000 Hp ·550 ft-lbs./ s- Hp · (time) = 0.5 · 69.4 slugs · ( 88 m/s)2 timesec = 0.49 Timesec = 0.49 seconds

Notice the only number that changed from the equation for the first car was the mass and as a result the time changed. Notice car2 has half the mass as car1, so it took half the time to accelerate 0-60 mph! The less mass, the easier to accelerate, so the less time needed to accelerate with a constant amount of power. In physics, we say that the time and power are directly related. Since these 4 numbers: 1000 Hp, 550 ft-lbs./ s- Hp , 0.5, and 88 ft/s are constants, the only numbers that will change are the mass and the time. We can set up a proportion.

Masscar 1 timecar 1

Masscar 2 = timecar 2

138.8 slugs 0.98 seconds

69.4 slugs = (timecar2)

Use this proportion to solve for timecar2 = ________ seconds

Answer 2

Gravity pulls objects down at the rate of 9.8 meters per second per second. This is invariable and weight nor mass has an effect on the rate that objects fall toward the earth. Tryit out...Drop a penny and a Baseball from a high spot and observe. They should hit the groud at the same time.

Answer 3

F = ma or a = F/m . Let m1 - mass of the heavier body and F1- the force required to produce an acceleration ' a ' in it, then a = F1/m1 ( 1). Let F2 be the force acting on a lighter body of mass m2 produces in it the same acceleration a , then a = F2/m2 (2)

since the accelerations are same from (1) and (2), F1/m1 = F2/m2 since m1 is greater than m2, F2 should be greater than F1 or F2 = F1* m2/m1.

Answer 4

Because the large mass NEEDS more force on it in order to get the same acceleration,

and the small mass NEEDS less force on it in order to get the same acceleration.

Since the large one HAS more force on it and the small one HAS less force on it,

the end result is that EVERY mass gets the same acceleration as long as they're

all on the same planet.

Answer 5

Larger cars will be using more fuel than the smaller cars on moving

Answer 6

by exerting more force on the car with the large mass than with the car with the small mass.

Answer 7

Because the force is proportional to the mass also, and when the formula for acceleration is used we find that acceleration due to gravity for all objects is equal.

Answer 8

If it has more mass, it requires more effort - more force, really - to accelerate it. With a greater mass, the same force would result in less acceleration.