An isolated rail car originally moving with speed $v_0$ on a straight, frictionles, level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car. What happens to the speed of the rail car as the sand pours out?
The car begins to roll faster
The car maintains the same speed
The car begins to slow down
The problem cannot be solved since momentum is not conserved
A force of $98\, N$ is required to just start moving a body of mass $100\, kg$ over ice. The coefficient of static friction is
A $1\,kg$ block is being pushed against a wall by a force $F = 75\,N$ as shown in the Figure. The coefficient of friction is $0.25.$ The magnitude of acceleration of the block is ........ $m/s^2$
A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is $\mu $. Let the mass of the box be $m$.
$(a)$ At what angle of inclination $\theta $ of the plane to the horizontal will the box just start to slide down the plane ?
$(b)$ What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to $\alpha > \theta $ ?
$(c)$ What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed ?
$d)$ What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration $a$ ?
A block of mass $2 \,kg$ is kept on the floor. The coefficient of static friction is $0.4$. If a force F of $2.5$ Newtons is applied on the block as shown in the figure, the frictional force between the block and the floor will be ........ $N$
A cyclist speeding at $18 \;km/h$ on a level road takes a sharp circular turn of radius $3\; m$ without reducing the speed. The co-efficient of static friction between the tyres and the road is $0.1$. Will the cyclist slip while taking the turn?