Answer:
15.8 ft/s
Explanation:
= Velocity of car A = 9 ft/s
a = Distance car A travels = 21 ft
= Velocity of car B = 13 ft/s
b = Distance car B travels = ft
c = Distance between A and B after 4 seconds = √(a²+b²) = √(21²+28²) = √1225 ft
From Pythagoras theorem
a²+b² = c²
Now, differentiating with respect to time
∴ Rate at which distance between the cars is increasing three hours later is 15.8 ft/s
<span>The maximum possible efficiency, i.e the efficiency of a Carnot engine , is give by the ratio of the absolute temperatures of hot and cold reservoir.
η_max = 1 - (T_c/T_h)
For this engine:
η_max = 1 - [ (20 +273)K/(600 + 273)K ] = 0.66 = 66%
The actual efficiency of the engine is 30%, i.e.
η = 0.3 ∙ 0.664 = 0.20 = 20 %
On the other hand thermal efficiency is defined as the ratio of work done to the amount of heat absorbed from hot reservoir:
η = W/Q_h
So the heat required from hot reservoir is:
Q_h = W/η = 1000J / 0.20 = 5000J</span>
See attached photos for the solution:
k is the rate constant
T is the absolute temperature (in kelvins)
A is the pre-exponential factor, a constant for each chemical reaction. According to collision theory, A is the frequency of collisions in the correct orientation
Ea is the activation energy for the reaction (in the same units as R*T)
R is the universal gas constant.
Answer:
Explanation:
The forces acting on the crates when the train starts stopping are their weights, the normal force from the train, the static frictional force and the fictional force that is produced by the deceleration of the train. As the gravitational force, this fictional force is equal to the mass of the crates multiplied by the magnitude of the acceleration of the train. So, the equations of motion of the crates will be:
Since the static frictional force is , we get:
So we have a limit to the acceleration of the train. Now, we have to know the distance traveled by the train when it is stopping. Then, we use the kinematic formula:
Now we solve for the acceleration to combine this equation to the inequality we got before:
And solve for x:
Since we are looking for the minimum value for x, we consider the case in which that inequality becomes an equation:
Before we finish, we have to convert the unities of the initial velocity to meters per second:
Finally, we plug in the known values to get :
It means that the train can be stopped at a minimum distance of 36.2m at constant acceleration without causing the crates slide over the floor.
Answer:
Explanation:
Given
Force=18lb
extension=8in
Using Hooke's law to get the spring constant(k)
F=ke
Then,
K=f/e
K=18/8
K=2.25lb/in
Work done by spring is given by
W=1/2Fe
Or W=1/2ke²
Then,
Work done in stretching the spring to 14in
W=1/2ke²
W=0.5×2.25×14²
W=220.5lbin
1 Inch-pounds Force to Joules = 0.113J
Then, to joules
W=0.133×220.5
W=29.33J