Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is $60.0$°. If Rover exerts a force of $270$ N and Fido exerts a force of $300$ N, find the magnitude of the resultant force and the angle it makes with Rover's rope.

To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E$4.2$. Find the $x$- and $y$-components of each of the three pulls.

To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E$4.2$. Use the components to find the magnitude and direction of the resultant of the three pulls.

Due to a jaw injury, a patient must wear a strap (Fig. E$4.3$) that produces a net upward force of $5.00$ N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

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A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of $20.0$°, and the man pulls upward with a force $\overrightarrow{F}$ whose direction makes an angle of $30.0$° with the ramp (Fig. E$4.4$). How large a force $\overrightarrow{F}$ is necessary for the component $F_x$ parallel to the ramp to be $90.0$ N?

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A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of $20.0$°, and the man pulls upward with a force $\overrightarrow{F}$ whose direction makes an angle of $30.0$° with the ramp (Fig. E$4.4$). How large will the component $F_y$ perpendicular to the ramp be then?

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You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. When the elevator has an upward acceleration of magnitude $2.50$ m/s², what does the scale read?

You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. If you hold a $3.85$-kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)? Note: Part (a) asked what does the scale read when the elevator has an upward acceleration of magnitude $2.50$ m/s².

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude $48.0$ N to the box and produces an acceleration of magnitude $2.20$ m/s², what is the mass of the box?

A dockworker applies a constant horizontal force of $80.0$ N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves $11.0$ m in $5.00$ s. What is the mass of the block of ice?

A hockey puck with mass $0.160$ kg is at rest at the origin ($x=0$) on the horizontal, frictionless surface of the rink. At time $t=0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$-axis; she continues to apply this force until $t=2.00$ s. What are the position and speed of the puck at $t=2.00$ s?

A hockey puck with mass $0.160$ kg is at rest at the origin ($x = 0$) on the horizontal, frictionless surface of the rink. At time $t = 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$-axis; she continues to apply this force until $t = 2.00$ s. If the same force is again applied at $t=5.00$ s, what are the position and speed of the puck at $t=7.00$ s?

A $4.50$-kg experimental cart undergoes an acceleration in a straight line (the $x$-axis). The graph in Fig. E$4.13$ shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

A $4.50$-kg experimental cart undergoes an acceleration in a straight line (the $x$-axis). The graph in Fig. E$4.13$ shows this acceleration as a function of time. During what times is the net force on the cart a constant?

A small $8.00$-kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation $F=A+B{t}^2$. Measurements show that at $t=0$, the force is $100.0$ N, and at the end of the first $2.00$ s, it is $150.0$ N. Find the constants $A$ and $B$, including their SI units.

An astronaut's pack weighs $17.5$ N when she is on the earth but only $3.24$ N when she is at the surface of a moon. What is the acceleration due to gravity on this moon?

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g=1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What is the watermelon's mass on the earth's surface?

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g = 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What would be its mass and weight on the surface of Io?

World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude $15$ m/s². How much horizontal force must a $55$-kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

A small car of mass $380$ kg is pushing a large truck of mass $900$ kg due east on a level road. The car exerts a horizontal force of $1600$ N on the truck. What is the magnitude of the force that the truck exerts on the car?

Boxes $A$ and $B$ are in contact on a horizontal, frictionless surface (Fig. E$4.23$). Box $A$ has mass $20.0$ kg and box $B$ has mass $5.0$ kg. A horizontal force of $250$ N is exerted on box $A$. What is the magnitude of the force that box $A$ exerts on box $B$?

Crates $A$ and $B$ sit at rest side by side on a frictionless horizontal surface. They have masses $m_A$ and $m_B$, respectively. When a horizontal force $F$ is applied to crate $A$, the two crates move off to the right. Draw clearly labeled free-body diagrams for crate $A$ and for crate $B$. Indicate which pairs of forces, if any, are third-law action–reaction pairs.

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.