Two $25.0$-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the rope?

Two $25.0$-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the chain?

A $75.0$-kg wrecking ball hangs from a uniform, heavy-duty chain of mass $26.0$ kg. What is the tension at a point three-fourths of the way up from the bottom of the chain?

A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to $0.75$ of the weight of the frame? (Ignore any friction between the wall and the picture frame.)

A large wrecking ball is held in place by two light steel cables (Fig. E$5.6$). If the mass m of the wrecking ball is $3620$ kg, what are the (a) tension $T_B$ in the cable that makes an angle of $40°$ with the vertical and (b) the tension $T_A$ in the horizontal cable?

Find the tension in each cord in Fig. E$5.7$ if the weight of the suspended object is $w$.

A man pushes on a piano with mass $180$ kg; it slides at constant velocity down a ramp that is inclined at $19.0°$ above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes parallel to the incline.

A man pushes on a piano with mass $180$ kg; it slides at constant velocity down a ramp that is inclined at $19.0°$ above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes parallel to the floor.

A $550$-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is $850$ kg. As the elevator starts moving, the scale reads $450$ N. Find the acceleration of the elevator (magnitude and direction).

An astronaut is inside a $2.25\times {10}^6$ kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound ($331$ m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than $4g$. What is the maximum initial thrust this rocket's engines can have but just barely avoid blackout? Start with a free-body diagram of the rocket.

An astronaut is inside a $2.25 × 10^6$ kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound ($331$ m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than $4g$. What force, in terms of the astronaut's weight $w$, does the rocket exert on her? Start with a free-body diagram of the astronaut.

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$-kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What was its acceleration (in m/s² and in g's), assumed to be constant, during the crash?

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$-kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight.

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E$5.14$). The pull is of magnitude $190$ N. Find the acceleration of the system.

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E$5.14$). The pull is of magnitude $190$ N. Find the tension in ropes $A$ and $B$.

An $8.00$-kg block of ice, released from rest at the top of a $1.50$-m-long frictionless ramp, slides downhill, reaching a speed of $2.50$ m/s at the bottom. What is the angle between the ramp and the horizontal?

An $8.00$-kg block of ice, released from rest at the top of a $1.50$-m-long frictionless ramp, slides downhill, reaching a speed of $2.50$ m/s at the bottom. What would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of $10.0$ N parallel to the surface of the ramp?

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. Draw two free-body diagrams: one for each block.

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. What is the acceleration of either block?

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. Find $m$.

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. How does the tension compare to the weight of the hanging block?

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. With what initial speed does the person leave the ground to reach a height of $60$ cm?

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. Draw a free-body diagram of the person during the jump.

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. In terms of this jumper's weight w, what force does the ground exert on him or her during the jump?

A $2.00$-kg box is moving to the right with speed $9.00$ m/s on a horizontal, frictionless surface. At $t=0$ a horizontal force is applied to the box. The force is directed to the left and has magnitude $F\left(t\right)=$ ($6.00$ N/s²)t². What distance does the box move from its position at $t=0$ before its speed is reduced to zero?

A $5.00$-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force $F\left(t\right)$ is applied to the end of the rope, and the height of the crate above its initial position is given by $y\left(t\right)=$ ($2.80$ m/s)t + ($0.610$ m/s³)t³. What is the magnitude of $F$ when $t=4.00$ s?

In a laboratory experiment on friction, a $135$-N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to increase thereafter. Figure E$5.26$ shows a graph of the friction force on this block as a function of the pull. Identify the regions of the graph where static friction and kinetic friction occur.

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it?

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. What is the magnitude of the friction force if a monkey applies a horizontal force of $6.0$ N to the box and the box is initially at rest?

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. What minimum horizontal force must the monkey apply to start the box in motion?