Answer:
204 m
Explanation:
When the marble is dropped from a certain height, its gravitational potential energy converts into kinetic energy. So the kinetic energy gained is equal to the variation of gravitational potential energy:
where
m is the mass of the marble
g = 9.8 m/s^2 is the acceleration of gravity
is the change in height
In this problem, we have
m = 50 g = 0.05 kg
Solving the formula for , we find the necessary height from which the marble should be dropped:
Answer:
63.5 °C
Explanation:
The expression for the calculation of work done is shown below as:
Where, P is the pressure
is the change in volume
Also,
Considering the ideal gas equation as:-
where,
P is the pressure
V is the volume
n is the number of moles
T is the temperature
R is Gas constant having value = 8.314 J/ K mol
So,
Also, for change in volume at constant pressure, the above equation can be written as;-
So, putting in the expression of the work done, we get that:-
Given, initial temperature = 28.0 °C
The conversion of T( °C) to T(K) is shown below:
T(K) = T( °C) + 273.15
So,
T₁ = (28.0 + 273.15) K = 301.15 K
W=1770 J
n = 6 moles
So,
Thus,
The temperature in Celsius = 336.63-273.15 °C = 63.5 °C
<u>The final temperature is:- 63.5 °C</u>
Answer:
Magnitude of avg velocity,
Given:
Constant speed of train, v = 79 km/h
Time taken in East direction, t = 27 min =
Angle,
Time taken in east of due North direction, t' = 29 min =
Time taken in west direction, t'' = 37 min =
Solution:
Now, the displacement, 's' in east direction is given by:
Displacement in east of due North for 29.0 min is given by:
Now, displacement in the west direction for 37 min:
Now, the overall displacement,
(a) Now, average velocity, is given:
Magnitude of avg velocity is given by:
(b) angle can be calculated as:
We are asked to determine the force required by the neck muscle in order to keep the head in equilibrium. To do that we will add the torques produced by the muscle force and the weight of the head. We will use torque in the clockwise direction to be negative, therefore, we have:
Since we want to determine the forces when the system is at equilibrium this means that the total sum of torque is zero:
Now, we solve for the force of the muscle. First, we add the torque of the weight to both sides:
Now, we divide by the distance of the muscle:
Now, we substitute the values:
Now, we solve the operations:
Therefore, the force exerted by the muscles is 23.53 Newtons.
Part B. To determine the force on the pivot we will add the forces we add the vertical forces:
Since there is no vertical movement the sum of vertical forces is zero:
Now, we add the force of the muscle and the weight to both sides to solve for the force on the pivot:
Now, we plug in the values:
Solving the operations:
Therefore, the force is 73.53 Newtons.