(a) Neglecting gravitational forces, what force would be re- quired to accelerate a $1200$-metric-ton spaceship from rest to one-tenth the speed of light in $3$ days? In $2$ months? (One metric ton $=1000$ kg.) (b) Assuming that the engines are shut down when this speed is reached, what would be the time required to complete a $5$-light-month journey for each of these two cases? (Use $1$ month $=30$ days.)

In a modified tug-of-war game, two people pull in opposite directions, not on a rope, but on a $25$-kg sled resting on an icy road. If the participants exert forces of $90$ N and $92$ N, what is the acceleration of the sled?

Two blocks are in contact on a frictionless table. A horizontal force is applied to one block, as shown in earlier Fig. $(a)$ If $m_1=2.3$ kg, $m_2=1.2$ kg, and $F=3.2$ N, find the force of contact between the two blocks. $(b)$ Show that if the same force $F$ is applied to $m_2$ rather than to $m_1$ , the force of contact between the blocks is $2.1$ N, which is not the same value de- rived in $(a)$. Explain.

A car with a mass of 1000.0 kg accelerates from 0 to 90.0 km/h in 10.0 s. (a) What is its acceleration? (b) What is the net force on the car?

What is the relation$—$if any$—$between the force acting on an object and the direction in which the object is moving?

A vertical force vector F is applied to a block of mass m that lies on a floor. What happens to the magnitude of the normal force F_N on the block from the floor as magnitude F is increased from zero if force vector F upward?

A rock is on an inclined surface. The rock is originally at rest, but starts to slide down the incline. The magnitude of the force on the surface due to the rock is $F_{SR}$ , and the magnitude of the force on the rock due to the surface is $F_{RS}$. If we com- pare these forces, we find
$(A)$ $F_{SR}<F_{RS}$. always. $(B)$ $F_{SR}=F_{RS}$ when the rock is at rest but then $F_{SR}>F_{RS}$. $(C)$ $F_{SR}=F_{RS}$ always. $(D)$ $F_{SR}>F_{RS}$ always.

Of the objects listed in earlier Table, which might be considered as a particle for the motion described? For those that behave like particles, can you describe a type of motion in which they could $\it{not}$ be considered as particles?

A $10.0$ kg object is launched vertically into the air with an initial velocity of $50.0$ m/s. In addition to the force of gravity there is a frictional force which is proportional to velocity ac- cording to $f_y=-bv_y$; note that this frictional force is nega- tive (down) when the object is moving up, but positive (up) when the object is moving down. (a) Numerically generate distance-time graphs for the object, using $b=0$, but use several different step sizes for $\Delta$ $t$, such as $1.0$ s, $0.1$ s, $0.01$ s, and $0.001$ s. Show the results on a sin- gle graph. How does the highest point vary with the step size? (b) Numerically generate distance-time graphs for the object, using a step size of $\Delta$ $t=0.01$ s. Now, however, try non-zero values for $b$, such as $0.1~\mathrm{N}~\cdot$ s/m, $0.5~\mathrm{N}~\cdot$ s/m, $1.0~\mathrm{N}~\cdot$ s/m, $5.0~\mathrm{N}~\cdot$ s/m and $10.0~\mathrm{N}~\cdot$ s/m. How does the highest point vary with $b?$ What do you notice about the shape of the graphs as $b$ increases?

Criticize the statement, often made, that the mass of a body is a measure of the “quantity of matter” in it.

Suppose that the Sun’s gravitational force was suddenly turned off, so that Earth became a free object rather than be- ing confined to orbit the Sun. How long would it take for Earth to reach a distance from the Sun equal to Pluto’s pres- ent orbital radius? (Hint: You will find some of the data you need in earlier Appendix.)

Vector $\vec{\boldsymbol{a}}$ has a magnitude of $5.2$ units and is directed east. Vector $\vec{\boldsymbol{b}}$ has a magnitude of $4.3$ units and is directed 35$\degree$ west of north. By constructing vector diagrams, find the mag- nitudes and directions of $(a)$ $\vec{\boldsymbol{a}}$ $+$ $\vec{\boldsymbol{b}}$, and $(b)$ $\vec{\boldsymbol{a}}$ $-$ $\vec{\boldsymbol{b}}$.

A car traveling at 53 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 65 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger’s upper torso, which has a mass of 41 kg?

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of $v_0 = 55 km/h$; your best deceleration rate has the magnitude a = 5.18 m/s². Your best reaction time to begin braking is T = 0.75 s. To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are 40 m and 2.8 s? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).