Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction,the magnitude of the minimum additional force needed is ........... $N$.

$A$ block of mass $M = 100 \, kg$ is pulled by a force $T$ at an angle of $37^{\circ}$ with the horizontal. The coefficient of friction between the block and the ground is $\mu = 1/3$. $A$ person of mass $m = 25 \, kg$ is standing on a platform and pulls the block with the force $T$. Find the maximum upward acceleration $a_{\max}$ of the person such that the block just starts to move.

$A$ parachutist with a total mass of $75 \,kg$ drops vertically onto sandy ground with a speed of $2 \,m/s$ and comes to a halt over a distance of $0.25 \,m$. The average force exerted by the ground on her is close to ............ $N$.

$A$ uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is $0.5$. If the cylinder is $4\, cm$ in diameter and $10\, cm$ in height,which of the following is the minimum acceleration of the cart needed to cause the cylinder to tip over? (Assume $g = 10\, m/s^2$)

If the net force on a system is zero,then:

Three forces $F_1=10\,N$,$F_2=8\,N$,and $F_3=6\,N$ are acting on a particle of mass $5\,kg$. The forces $F_2$ and $F_3$ are applied perpendicular to each other such that the particle remains at rest. If the force $F_1$ is removed,then the acceleration of the particle is $......\,m/s^2$.