A 3.00 kg box that is several hundred meters above the earth’s surface is suspended from the end of a short vertical rope of negligible mass. A time-dependent upward force is applied to the upper end of the rope and results in a tension in the rope of T(t) = (36.0 N>s)t. The box is at rest at t = 0. The only forces on the box are the tension in the rope and gravity. (a) What is the velocity of the box at (i) t = 1.00 s and (ii) t = 3.00 s? (b) What is the maximum distance that the box descends below its initial position? (c) At what value of t does the box return to its initial position?

The distance between two telephone poles is d = 54.0 m. When a 1.20 kg bird lands on the telephone wire midway between the poles, the wire sags h = 0.206 m. (a) Draw a free-body diagram of the midpoint of the wire (where the bird is perched). mg O X* (b) How much tension (in N) does the bird produce in the wire? Ignore the weight of the wire. 3.15 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N Need Help? Read It

A mass, M = 8.6 kg hangs from a string of length L = 1.26 m.  The ball is pulled back so the string makes an angle 12.16 degrees with respect to the vertical and the ball is released.  The ball takes 0.69757232087945 seconds to reach its lowest point.  Determine the Tension, T, in the string at the lowest point.

a 1.34 kg ball is connected by means of two massless strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N. What are the (a) tension in the lower string, (b) magnitude of the net force  on the ball, and (c) speed of the ball? (d) What is the direction of the net force?

A 35.0-kg child swings in a swing supported by two chains, each 2.98 m long. The tension in each chain at the lowest point is 440 N. (a) Find the child's speed at the lowest point.m/s(b) Find the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)N (upward)

In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle 8 = 22.8°. The slab has length L = 48.9 m, thickness T = 6.61 m, and width W = 12.7 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.312. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.47 cm² and will snap under a shearing stress of 3.59 x 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.

.: A chandelier is suspended by two identical, vertical chains side by side. The chandelier's mass is m = 6.5 kg. Part (a) If the tension in one chain is represented by 7, write an expression for the magnitude of the tension in terms of m and g, the gravitational acceleration on the Earth's surface. T= a B 8 ( HOME 7 8 9 4 5 6 b d h 1 1 2 3 k m 0 END S t NO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Part (b) What is the tension in one chain, 7, in newtons? Part (c) If the tops of the chains are separated so that the chains are no longer vertical, does the tension increase or decrease? a g 1 P

Students are performing an experiment with the setup shown above, where a block of mass M sits on a horizontal table. The coefficient of kinetic friction between the block and the table is μk. The block is connected to a hanging object over a pulley. The pulley has negligible mass and friction. The string connecting the two is very light and does not stretch. The students add mass to the hanging object so that its mass is m, where m < M, and the block-hanging object system is released from rest. The hanging object falls for a distance h, at which point it collides with the ground and comes to rest. The block on the table keeps sliding and travels a total distance d before coming to rest. It does not reach the pulley, and d > h. A student creates a data table (see image) for the net force exerted on the block during the speeding up and slowing down portions of the experiment. (d) Does the block of mass M spend more time speeding up or slowing down? Justify your answer.

There are two forces on the 2.26 kg box in the overhead view of the figure but only one is shown. For F₁ = 12.6 N, a = 11.5 m/s², and 0 = 24.4°, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) a direction. (State the direction as a negative angle measured from the +x direction.) (a) Number i (b) Number i (c) Number i + i Units Units F x Ĵ Units î î

In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle θ = 28.4°. The slab has length L = 32.4 m, thickness T = 5.92 m, and width W = 14.3 m, and 1.0 cm3 of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.385. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.05 cm2 and will snap under a shearing stress of 3.34 × 108 N/m2, what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.