The $9\ kg$ block shown below is at rest.

The size of angle $θ$ is,

Two blocks are at rest over a rough surface whose coefficient of friction $μ_s$ is $0.3$.

The minimum force $F$ needed to set the system of blocks in motion is,

The same two blocks are now placed on a smooth table so that friction between the blocks and the table is negligible. A force $F = 48 \ N$ is applied to the $4 \ kg$ block as shown in the diagram. What is the magnitude and direction of the force the $8 \ kg$ block applies to the $4 \ kg$ block?

Calculate the average force acting on a block of mass $6.2\ kg$ if it accelerates from rest to $28\ m/s$ in $5.2 \ s$.

A block of mass $m$ accelerates to a speed $v_f$ from rest in time $t$. Determine the magnitude of the net force $F$ necessary to accelerate the same block of mass $m$ from rest to a speed $3_{vf}$ in time $t$ in terms of $m$, $v_f$, and $t$.

A car travels along a road that has 3 sections. The first section is a semicircular hill with a radius $R$, the next section is a flat section that passes through point $B$, and the third section is a semicircular dip with radius $R$. The car drives at a constant speed across all parts of the road. Which of the following correctly describes the relative magnitude of the Normal Force at points $A$, $B$, and $C$?

Starting from rest, a block of mass $m = 2 \ kg$ slides down a rough incline 10 meters in length that makes an angle $\theta = 30°$ with the horizontal. The coefficient of kinetic friction between the block and the rough ramp is $\mu k = \ 0.22$. How much less time would it take for the block to travel the same 10 meter distance along the ramp if the ramp was smooth so that friction between the block and ramp was negligible?

The two springs shown in the diagram have identical natural length and spring constant, $k$. The springs are both unstretched when $x = 0$ in the diagram below.

What is the net acceleration of the mass when it is displaced slightly from the rest position by $x$?

A block of mass m hangs from a string attached to the ceiling of an elevator. As the elevator accelerates upward with constant acceleration a, what is the magnitude of the magnitude of the tension in the rope?

Two blocks are connected together as shown above. The mass of the rope, mass of the pulley, friction within the pulley, and friction between the blocks and the ramp, are all negligible. Determine the mass of block $M$ in terms of $m$, $g$, and $\theta$ so that the system remains at rest.

Two blocks are connected together as shown above. The mass of the rope, mass of the pulley, friction within the pulley, and friction between the blocks and the ramp, are all negligible. The system is initially held in place by an external force (not shown). When released, the system begins to move so that the block of mass $2m$ begins to accelerate down the incline. Determine the acceleration of the blocks and rope system in terms of $m$, $g$, and $\theta$.

Two blocks, one of mass $5m$ and the other of mass $3m$, are connected together by a massless rope that is wrapped across the top of a massless pulley. The pulley hangs from a support rope and spins freely without friction in the bearing. The system is released from rest so that the $5m$ block descends and accelerates downward. Which of the following is true about the Tension in the rope connecting the $5m$ and $3m$ blocks as the $5m$ block descends?

A marble of mass $m_1$, tied to a string, performs uniform circular motion.

A block of mass $m_2$ is attached to the other end of the string. The velocity of the marble at which the tension force of the string is enough to balance the weight of the block is,

Two satellites, one of mass $m$, the other of mass $2m$, are both in circular orbits around the Earth. The radius of the satellite of mass $m$ is $2R$, while the satellite of mass $2m$ has an orbital radius of $3R$. What is the ratio of the gravitational force exerted on the satellite in the closer vs farther orbit?

Andrew draws a schematic diagram for astronomical objects.

What is the net gravitational force acting on the heavier object?

A block of mass m spins in a vertical circle of radius $R$. What minimum speed must the block maintain at the top of the loop in order to follow this circular path? Express your answer in terms of $m$, $R$, and fundamental constants.

A book weighs $28\ N$ on the surface of the Earth. What is the weight of the book on another planet whose radius is twice that of Earth and Mass thrice that of Earth?

Two planets, A and B, both orbit the same star while following circular orbits. Planet A has a mass of $M$ and follows an orbit of radius $R$ and period $T$. Planet B has a mass of $2M$ and follows an orbit of radius $2R$. What is the ratio of the period for the orbit of Planet B to that of Planet A?