In a Broadway performance, an 80.0-kg actor swings from a3.75-m-long cable that is horizontal when he starts. At the bottomof his arc, he picks up his 55.0-kg costar in an inelasticcollision. What maximum height do they reach after theirupward swing?

A 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P6.27 (page 188). Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2, = 3 400 N/m. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the cars initial speed.

An object of mass m is suspended from the top of a cart by a string of length L as in Figure P5.88a. The cart and object are initially moving to the right at a constant speed 0. The cart comes to rest after colliding and sticking to a bumper, as in Figure P5.88b, and the suspended object swings through an angle . (a) Show that the initial speed is 0=2gL(1cos). (b) If L = 1.20 m and = 35.0, find the initial speed of the cart (Hint: The force exerted by the string on the object docs no work on the object.) Figure P5.88a

Repeat the preceding problem, but including a drag force due to air of fdrag=bv .

A block of mass m1 = 4.00 kg initially at rest on top of a frictionless, horizontal table is attached by a lightweight string to a second block of mass m2 = 3.00 kg hanging vertically from the edge of the table and a distance h = 0.450 m above the floor (Fig. P8.77). If the edge of the table is assumed to be frictionless, what is the speed with which the first block leaves the edge of the table?

You hold a slingshot at arms length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 200 cm/s. With the same procedure, you fire a bean with speed 600 cm/s. What is the ratio of the mass of the bean to the mass of the pebble? (a) 19 (b) 13 (c) 1 (d) 3(e) 9

A 1.00-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P8.62a). The object has a speed of vi = 3.00 m/s when it makes contact with a light spring (Fig. P8.62b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Fig. P8.62c). The object is then forced toward the left by the spring (Fig. P8.62d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Fig. P8.62e). Find (a) the distance of compression d, (b) the speed vat the unstretched posi-tion when the object is moving to the left (Fig. P8.624), and (c) the distance D where the abject comes to rest. Figure P8.62

A Small pickup truck that has a caliper shell slowly coasts toward a red light with negligible friction. Two dogs in the back of the truck are moving and making various inelastic collisions with each other and the walls. What is the effect of the dogs on the motion of the center of mass of the system (truck plus entire load)? What is their effect on the motion of the truck?

Two objects are connected by a light string passing over a light, frictionless pulley as shown in Figure P7.7. The object of mass m1 = 5.00 kg is released from rest at a height h = 4.00 m above the table. Using the isolated system model, (a) determine the speed of the object of mass m2 = 3.00 kg just as the 5.00-kg object hits the table and (b) find the maximum height above the table to which the 3.00-kg object rises.

To get up on the roof, a person (mass 70.0 kg) places 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to frictionless. The center of ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.