This is not as simple as it looks.
His average speed is NOT (10km/hr + 50km/hr)/2 = 30 km/hr.
You have to use the definition of speed:
Speed = (total distance covered) / (time to cover the distance).
Let's say the distance up (and down) the hill is 'd' .
Then the time it takes to go up the hill is (d/10) hours.
And the time it takes to come down the hill is (d/50) hours.
Total distance = 2d km
Total time = (d/10) + (d/50) = (5d/50) + (d/50) = 6d/50
Speed = distance/time = 2d/(6d/50) = 100d/6d
<em>Speed = </em>100/6 = <em>16-2/3 km/hr</em>
Answer:
Force = 186 N
Explanation:
Torque is the rotational equivalent of linear force. It can be easely calculated using the formula :

Where
is a vector that from the origin of the coordinate system to the point at which the force is applied (the position vector),
is the applied force.
The easiest way of computing the force is by setting the origin of the coordinate system to the lowest point of the torque wrench. By doing this we have that
(the magnitud of the position vector) is 35cm.
Before computing the force we need to set all our values to the international system of units (SI). The torque is already in SI. The one missing is the length of the torque wrench (it is in centimeters and we need it in meters). So :
Now using the torque formula:


Where
is the smaller angle between the force and the position vector. Because the force is applied perpendiculary to the position vector
, thus :





so the force is approximately 186 N.
Explanation:
(a) We have,
Length of solenoid, l = 55 cm = 0.55 m
Diameter of the solenoid, d = 10 cm
Radius, r = 5 cm = 0.05 m
Number of loops in the solenoid is 1000.
(a) The self inductance in the solenoid is given by :

A is area

(b) The energy stored in the inductor is given by :

Hence, this is the required solution.