Slider $C$ has a weight of $0.5 \mathrm{lb}$ and may move in a slot cut in arm $A B$, which rotates at the constant rate $\theta_0=10 \mathrm{rad} / \mathrm{s}$ in a horizontal plane. The slider is attached to a spring of constant $k=2.5 \mathrm{lb} / \mathrm{ft}$, which is unstretched when $r=0$. Knowing that the slider is released from rest with no radial velocity in the position $r=18$ in. and neglecting friction, determine for the position $r=12 \mathrm{in}$. (a) the radial and transverse components of the velocity of the slider, $(b)$ the radial and transverse components of its acceleration, $(c)$ the horizontal force exerted on the slider by arm $A B$.

A small, $200-\text{g}$ collar $D$ can slide on portion $A B$ of a rod which is bent as shown. Knowing that the rod rotates about the vertical $A C$ at a constant rate and that $\alpha=30^{\circ}$ and $r=600 \mathrm{~mm}$, determine the range of values of the speed $v$ for which the collar will not slide on the rod if the coefficient of static friction between the rod and the collar is $0.30$.

A small $250~\mathrm{g}$ collar $C$ can slide on a semicircular rod which is made to rotate about the vertical $A B$ at a constant rate of $7.5$ rad/s. Knowing that the coefficients of friction are $\mu_s=0.25$ and $\mu_k=0.20$, indicate whether the collar will slide on the rod if it is released in the position corresponding to $(a)$ $\theta=75^{\circ}$, $(b)$ $\theta=40^{\circ}$. Also, determine the magnitude and direction of the friction force exerted on the collar immediately after release.

During a hammer thrower's practice swings, the $7.1-\text{kg}$ head A of the hammer revolves at a constant speed $v$ in a horizontal circle as shown. If $\rho=0.93 \mathrm{~m}$ and $\theta=60^{\circ}$, determine $(a)$ the tension in wire $B C,(b)$ the speed of the hammer's head.

The parasailing system shown uses a winch to let rope out at a constant rate so that the $70 \mathrm{~kg}$ rider moves away from the boat, which is traveling with a constant velocity. At the instant shown, the rope has a length of $30 \mathrm{~m}$, it is increasing in length at a constant $1 \mathrm{~m} / \mathrm{s}$, the angle is increasing at a rate of $0.05 \mathrm{rad} / \mathrm{s}$, and $\ddot{\theta}$ is $-0.01 \mathrm{rad} / \mathrm{s}^2$. Knowing that when the rope makes a $30^{\circ}$ angle with respect to the water, the tension in the rope is $10 \mathrm{kN}$, determine the magnitude and direction of the force of the parasail on the parasailor.

The slotted arm rotates about its center in a horizontal plane at the constant angular rate $\dot{\theta}=10$ rad/sec and carries a 3.22-lb spring-mounted slider which oscillates freely in the slot. If the slider has a speed of 24 in./sec relative to the slot as it crosses the center, calculate the horizontal side thrust P exerted by the slotted arm on the slider at this instant. Determine which side, A or B, of the slot is in contact with the slider.

A small $250~\mathrm{g}$ collar $C$ can slide on a semicircular rod which is made to rotate about the vertical $A B$ at a constant rate of $7.5$ rad $/ \mathrm{s}$. Determine the three values of $\theta$ for which the collar will not slide on the rod, assuming no friction between the collar and the rod.

The position of the $10 \mathrm{~lb}$ machine block $B$ is adjusted by moving the $5 \mathrm{~lb}$ wedge $A$. Neglect friction between all surfaces of contact. Knowing that $\mathbf{P}=$ $10 \mathrm{~lb}$, determine the $(a)$ acceleration of $B$, $(b)$ force between $A$ and $B$.

The coefficients of friction between the load and the flatbed trailer shown are $\mu_{s}=0.40$ and$\mu_{s}=0.30$. Knowing that the speed of the rig is 72 km/h, determine the shortest distance in which the rig can be brought to a stop if the load is not to shift.

A child throws a ball from point $A$ with an initial velocity $\mathbf{v}_0$ at an angle of $3^{\circ}$ with the horizontal. Knowing that the ball hits a wall at point $B$, determine $(a)$ the magnitude of the initial velocity, $(b)$ the minimum radius of curvature of the trajectory.

A child throws a ball from point $A$ with an initial velocity $\mathbf{v}_A$ of $20 \mathrm{~m} / \mathrm{s}$ at an angle of $25^{\circ}$ with the horizontal. Determine the velocity of the ball at the points of the trajectory described by the ball where the radius of curvature is equal to three-quarters of its value at $A$.

Pin $A$, which is attached to link $A B$, is constrained to move in the circular slot $C D$. Knowing that at $t=0$ the pin starts from rest and moves so that its speed increases at a constant rate of $0.8 \mathrm{~in} / \mathrm{s}^2$, determine the magnitude of its total acceleration when $(a)$ $t=0$, $(b)$ $t=2 \mathrm{~s}$.

A robot arm moves in the vertical plane so that the $0.1 \mathrm{~kg}$ cylinder $P$ travels in a circle about point $B$, which is not moving. Knowing that arm $B P$ starts from rest in a horizontal position, and that the speed of $P$ increases at a constant rate of $200 \mathrm{~mm} / \mathrm{s}^2$, determine the force acting on the cylinder at $t=3 \mathrm{~s}$.

The speed of a satellite launched into a circular orbit about the earth is given by $v_c=\sqrt{\frac{G M_e}{r_0}}$. Determine the speed of a satellite launched parallel to the surface of the earth so that it travels in a circular orbit $800 \mathrm{~km}$ from the earth's surface.