Why are mountain roads generally made winding upwards rather than going straight up?
Answer
On an inclined plane force of friction on a body going upward is $\text{f}_\text{s}=\mu\text{N}\cos\theta$ where $\theta$ is angle of inclination of a plane with horizontal if $\theta$ is small, the force of friction is high and there is a less chance of skidding. The road straight up would have a larger angle and smaller would be the value of friction, hence more are the chances of skidding.
Give the magnitude and direction of the net force acting on. A car moving with a constant velocity of 30km/h on a rough road.
Answer
Force is being applied to overcome the force of friction. But as velocity of the car is constant, its acceleration, a = 0. Hence net force on the car F = ma = 0.
A body is dropped from the ceiling of a transparent cabin falling freely towards the earth. Describe the motion of the body as observed by an observer $(a)$ sitting in the cabin $(b)$ standing on earth.
Answer
Appears stationary in the lift.
Appears to fall freely $\Big(\text{a}=\frac{\text{g m}}{\text{s}^2}\Big)$
A mass m moving with a velocity u hits a surface at an angle $\theta$ with the normal at the point of hitting. How much force does it exerts, if no energy is lost?
Answer
Force = Rate of change in momentum $=\frac{2\text{mu}\cos\theta}{\text{time}}$ $\because\ \text{mu}\cos\theta$ is momentum along the normal at the point of incidence.
The mountain road is generally made winding upwards rather than going straight up. Why?
Answer
When we go up a mountain, the opposing force of friction $\text{F}=\mu\text{R}=\mu\text{mg}\ \cos.$ where $\theta$ is angle of slope with horizontal. To avoid skidding, F should be large. $\therefore\cos\theta$ should be large and hence, 0 must be small. Therefore, mountain roads are generally made winding upwards. The road straight up would have large slope.
It is easier to pull lawn roller than to push it. Why?
Answer
When we pull a lawn mover the vertical component of applied pull acts opposite to the weight of mover and it reduces the effective weight on the other hand. When the lawn mover is pushed vertical component of applied push adds to the weight of mover and therefore its effective weight is more than actual.
A retarding force is applied to stop a motor car. If the speed of the motor car is doubled, how much more distance will it cover before stopping under the same retarding force?
Answer
Retarding force is same. For the same car, the mass is same. So the deceleration is same. We know that v = 0, $\text{u}\neq0.$ Using $v^2 - u^2 = 2as$ we have $\text{s}=\frac{\text{u}^2}{2\text{a}}.$ So doubling the speed will make the distance increase to four times.
Give the magnitude and direction of the net force acting on. A high-speed electron in space far from all material objects, and free of electric and magnetic fields.
Answer
As the high speed electron in space is far away from all gravitating objects and free of electric and magnetic fields, the net force on electron is 0.
A heavy point mass tied to the end of string is whirled in a horizontal circle of radius 20cm with a constant angular speed. What is angular speed if the centripetal acceleration is $980cm/ s^{-2}$?
Answer
Here, radius r = 20cm Centripetal acceleration, = $980cm/ s^{-2}$ We know that centripetal acceleration, $\text{a}=\text{r}\omega^2$ $\omega=\sqrt{\frac{\text{a}}{\text{r}}}=\sqrt{\frac{980}{20}}$ $\omega=\sqrt{49}=7\text{rad/ }\text{s}$
Why do aeroplanes having wings fly at low altitudes?
Answer
The wings of aeroplane push the air backwards and the reaction of the air pushes the plane forward. At low altitudes, air is dense and as such the reaction of the air on plane is large.
One often comes across the following kind of statement concerning circular motion. A particle moving uniformly along a circle experiences a force directed towards the centre and an equal and opposite force directed away from the centre. The two forces together keep the particle in equilibrium. Explain, what is wrong with this statement?
Answer
This statement is wrong relative to any inertial frame of reference that we normally use (e.g., laboratory frame that is approximately inertial). The particle in circular motion is not in equilibrium, it has a centripetal acceleration. Centrifugal force does not exist relative to an inertial frame. The statement is correct relative to the (non-inertial) frame rotating with the particle.
A ball moving with a momentum of $5kg~ms^{-1}$ strikes against a wall at an angle of 45° and is reflected at the same angle and with same speed. Find the change in momentum of the ball.
Answer
$\Delta\text{p}=2\text{ mv}\cos\theta$$=2\times5\times\cos45^\circ$
$=5\sqrt{2}\text{ kg m/s}$