Mech-ing

Given data: Mass of the car (m) = 500 kg, Speed of the car (u) = 36 km/h, time required to stop the car (t) = 10 s. Find acceleration of the car after applying break to write the equation of the uniform acceleration. v = u + at  ......(1) Here, v is the speed of the car after car stopped i.e. 0 m/s  and a is the acceleration of the car. Convert speed of the car from  km/h to m/s. u = 36 × (1000/3600) u = 10 m/s Substitute 10 m/s for u, 10 s for t and 0 m/s for v in the equation (1). 0 = 10 + (10a) a = -1 m/s² According to defination of the force, write the equation of the force. F = ma Substitute -1 m/s² for a and 500 kg for m  in the above equation. F = (-1 ×500) F = -500 N The negative sign represents that this force opposes the motion of the car. Thus, the brake force required to stop the car is 500 N.

As shown in figure, torque is dependent on distance at where force is applied and force. It means that torque can be incresead or decreased by changing the distance or force. Let's look in to the formula of torque. Torque= Force × Distance  Now if you have two forces with different magnitudes, you can create same torque by changing distance accordingly. Let's take an example, there are two forces F' and F" as F'<F". And it is needed to torque from force F'  which is more than F",  we need to increase the distance of F'  accordingly as it creates larger torque than F".

Given data: Total length of travelling (d) = 285 km Speed of the bus (u) = 40 km/h Speed of the train (v) = 55 km/h Time of the travelling (t) = 6h To find the expression of the distance travelled by the bus, write the equation of the speed of bus. u=x/t' Here, a x is the distance travelled by the bus and t' is the time of travelling by the bus. Rearrange the above equation. x=u × t' Substitute 40 km/h for u  in the above equation. x=40t' ......(1) Similarly, distance travelled by train can be expressed as, y=55t".....(2) Here, t"  is the time of travelling by train. Here, total distance can be expressed as, d= x + y Substitute 40t' for x, 55t"  for y, and 285 km  for d in the above equation. 285=40t' + 55t"  ......(3) And total time of the journey can be expressed as, t= t' + t" Substitute 6 h  for t  in the above equation. 6=t' + t" ......(4) Solving equation (3) and (4), we get, t' = t" = 3 h Substitute 3 h  in t...

Here, a bike starts from the rest, it means, initially, bike has zero velocity. Mathematically it can be written as, u=0 m/s Aftet traveling distance of 34.3 m, bike has a velocity of 8.20 m/s.  Mathematically it can be written as, v=8.20 m/s after d=34.3m Write the equation of uniform acceleration. v² + u² = 2ad Here, a  is acceleration of the bike. Substitute 0 m/s for u,   8.20 m/s for u  and 34.3 m for d  in the above equation. (8.20)² +(0)² = 2a(34.3) a=0.980 m/s² Thus, the acceleration of the bike is 0.980 m/s².

Firts trains crosses the person within 8 seconds. So the equation of speed of train can be written as, v=x/8   ......(1) Here, x is the length of the train. And the train crosses the bridge of 180m within 20 seconds. So the equation of the speed of train can also be written as,  v=(x + 180)/20   ......(2) Equalise the equation (1) and (2) . 20x=8x+1440 12x =1440 x=120 m Substitute 120 m for x  in the equation (1) . v=15 m/s Thus, the speed of the train is 15 m/s .

 Here, first it is needed to understand definitions of the velocity and acceleration. Velocity is the change in displacement per unit time. And acceleration is the change in velocity per unit time. It is noted that displacement is a vector quantity, thus, ultimately velocity and acceleration are also vector quantities.  It means velocity can be changed with time by magnitude or direction. While a substance is rotating about any center with velocity 'v' which magnitude is uniform. But due to rotational motion, the direction of the velocity is changing continuously. This cause the acceleration which is radially . And this know as centrifugal acceleration. When substance is tied by string to the centre, then there is a reaction force is produced to oppose the centrifugal force, which is known as centripetal force. This centripetal force causes the centripetal acceleration which is radially inward. 

Question:  A solid shaft is transmitting 2 MW at 270 r.p.m. Determine the diameter of the shaft. Take the maximum allowable shear stress as 72 MPa. Answer: Given data: Power transmitted by the shaft ( P ) = 2 MW,  Speed of the shaft ( N ) = 270 rpm, The maximum allowable shear stress  = 72 MPa. To calculate mean torque. Substitute 2 MW for P and 270 rpm for N   in the above equation. Write the equation of the shear stress. Here, d   is the diameter of the shaft. Rearrange the above equation. Substitute 70735.530 N-m for   , 72 MPa for   in the above equation. Thus, the diameter of the shaft is 171.038 mm.