Usually, we do not walk or even stand on a lightweight boat or raft because of the danger of falling into the water. If you have ever stepped off a small boat onto a dock, however, you have probably noticed that the boat moves away from the dock as you step toward the dock or out of the boat. A heavy dog running on a long lightweight raft presents a similar situation. At first, the raft and the dog are at rest with respect to the water (see figure A below) so that  vi = 0.  The dog then runs on top of the raft at  vd = vd  with respect to the water (see figure B below). The dog has half the mass of the raft. Find an expression for the velocity of the raft after the dog began running. (Use the following as necessary: vd.)

A physics demonstration includes golf balls placed on top of paper tubes resting on a cookie sheet that is sitting on three glass beakers filled with water.  A force is applied to the cookie sheet that causes it to accelerate forward (to the left in this picture), off the beakers.  The golf balls resting on the paper tubes fall down into the beakers filled with water while the paper tubes move with the cookie sheet and do not land in the beakers.  Choose the best explanation for this observation.

A ball of mass m = 1.55 kg is released from a height of h = 2.8 m into a tank of water. At a time of t = 1.08 s after hitting the surface of the water, the ball's velocity has decreased by 50%. 1) What is the magnitude of the average force the ball experiences, in newtons, during the time t?

The figure shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0 container 1 has mass 1.2 kg and container 2 has mass 2.7 kg, but container 1 is losing mass (through a leak) at the constant rate of 0.21 kg/s. At what rate is the acceleration magnitude of the containers changing at (a)t = 0 and (b)t = 5 s? (c) When does the acceleration reach its maximum value? (a) Number (b) Number (c) Number Units Units Units Click if you would like to Show Work for this question: Open Show Work

A hockey puck with mass 0.225 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of an ice rink. At time t = 0 a player applies a force of 9.50 N on the puck, parallel to the positive x- axis. She continues to apply this force until t = 0.850s. What are the position and speed of the puck at t = 0.850 s?

Block A with a mass of 1.2 kg is at rest on a flat, horizontal, frictionless table 1 m from the edge. A string is tied to Block A at one end, and the other is tied to Block B, which has a mass of 2.6 kg. While Block A is being held in place on the table, Block B is lowered over the edge of the table and allowed to hang freely. When Block A is released, it slides to the edge of the table. Assume that the string has an insignificant mass. How much time does it take for Block A to reach the edge of the table?

A 10.0 kg mass is acted on by the two forces:   and  F1=(3.0N)i+(2.0N)j and F2=(10.0N)i+(7N.0)7 a) Express the summation of these two forces in unit vector notation.  That is:   b) What is the acceleration of this mass while these forces are acting? Write your answer in unit vector notation.  c)  What is the direction of the acceleration (give the angle of acceleration with the x axis)?

Two objects (m1=11.0 kg and m2=3.00 kg) are separated by 40.0 cm. A third object (m3=1.00 kg) is placed at a location along the line connecting them such that the net force acting on it is zero. By considering the force vectors, this location must be between the two original objects. We will define x as the distance between m1 and m3 and y as the distance between m2 and m3.   1) Find the distance between 11.0-kg object and 1.00-kg object along the line AB where a small, 1.00-kg object could rest such that the net gravitational force on it due to the two objects shown is exactly zero. (Express your answer to two significant figures.)

A small object is initially at rest at the top of a large solid sphere that is fixed on the ground. The small object then begins to slide along the surface of the large solid sphere, without friction. V₁ = 0 RI Part (a) Find the angle at which the small object loses contact with the large solid sphere. Part (b) Find the maximum horizontal distance traveled by the small object before it hits the ground. Take (xi, y₁) = (0,2R) as the coordinates for the top of the large solid sphere.

On a horízontal air track, a glider of mass m carries a l-shaped post. The post supports a small dense sphere, also of mass m, hanging just above the top of the glider on a cord of length L. The glider and sphere are initially at rest with the cord vertical. (Figure a below shows a cart and a sphere similarly connected.) A constant horizontal force of magnitude F is applied to the glider, moving it through displacement x;; then the force is removed. During the time interval when the force is applied, the sphere moves through a displacement with horizontai component x2. (a) Find the horizontal component of the velocity of the center of mass of the glider-sphere system when the force is removed. (Use the following as necessary: F, x1, x2, and m.) F(x, +x2) VCM 2m (b) After the force is removed, the glider continues to move on the track and the sphere swings back and forth, both without friction. Find an expression for the largest angle the cord makes with the vertical. (Use any variable…