91Ó°ÊÓ

Vector $A$has y-component $Ay=+9.60m$. A makes an angle of $32.0$ counterclockwise from the +y-axis. (a) What is the x-component of $A$ ? (b) What is the magnitude of $A$ ?

A little red wagon with mass 7.00 kg moves in a straight line on a frictionless horizontal surface. It has an initial speed of 4 m/s and then is pushed 3.0 m in the direction of the initial velocity by a force with a magnitude of 10.0 N. (a) Use the work energy theorem to calculate the wagon’s final speed.

(b) Calculate the acceleration produced by the force. Use this acceleration in the kinematic relationships of Chapter 2 to calculate the wagon’s final speed. Compare this result to that calculated in part (a)

At launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h; at the end of the first 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in m/s²) of the rocket (i) during the first 8.00 s and (ii) between 8.00 s and the end of the first 1.00 min? (b) Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel (i) during the first 8.00 s and (ii) during the interval from 8.00 s to 1.00 min?

A playground marry-go-round has radius 2.40 m and moment of inertia 2100 kg m2 about a vertical axle through its center, and it turns with negligible friction. (a) A child applies an 18.0-N force tangentially to the edge of the merry-go-round for 15.0 s. If the merry-go-round is initially at rest, what is its angular speed after this 15.0-s interval? (b) How much work did the child do on the merry-go-round? (c) What is the average power supplied by the child?

In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg from a vertical steel wire 0.50 m long and $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathit{c}{\mathit{m}}^{\mathbf{2}}$in cross-sectional area. On the bottom of the sphere he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0 kg. For each wire, compute (a) the tensile strain and (b) the elongation.

An ore sample weighs 17.50 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.20 N. Find the total volume and the density of the sample.

A 45.0-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0 m/s . (a) What are the coefficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of $\mathbf{1}\mathbf{.}\mathbf{10}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$? (c) Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is $\mathbf{1}\mathbf{.}\mathbf{62}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$. (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?

Question: A 45.0-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0m/s. (a) What are the coefficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of $\mathbf{1}\mathbf{.}\mathbf{10}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$? (c) Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is $\mathbf{1}\mathbf{.}\mathbf{62}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$. (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?

In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg from a vertical steel wire 0.50 m long and $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathit{c}{\mathit{m}}^{\mathbf{2}}$in cross-sectional area. On the bottom of the sphere he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0 kg. For each wire, compute (a) the tensile strain and (b) the elongation.

2. (a) Is it possible for an object to be in translational equilibrium (the first condition) but not in rotational equilibrium (the second condition)? Illustrate your answer with a simple example. (b) Can an object be in rotational equilibrium yet not in translational equilibrium? Justify your answer with a simple example.