An object is free to move on a table, except that there is a constant frictional force $f$ that opposes the motion of the ob- ject when it moves. If a force of $10.0$ N pulls the object, the acceleration is $2.0$ m/s$^2$. If a force of $20.0$ N pulls the object, the acceleration is $6.0$ m/s$^2$.
$(a)$ What is the force of friction $f?$ $~~~~(A)$ $1.0$ N. $(B)$ $3.33$ N. $(C)$ $5.0$ N. $(D)$ $10.0$ N. $(b)$ What is the mass of the object? $~~~~(A)$ $0.40$ kg. $(B)$ $2.5$ kg. $(C)$ $3.33$ kg. $(D)$ $5.0$ kg.

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.

An object is tossed into the air vertically from ground level with initial velocity

$$v _ { 0 }$$

ft/s at time t = 0. Find the average speed of the object over the time interval [0, T], where T is the time the object returns to Earth.

For each graph of velocity as a function of time, sketch a qualitative graph of the acceleration as a function of time.

An interstellar spacecraft, far from the influence of any stars or planets, is moving at high speed under the influence of fu- sion rockets when the engines malfunction and stop. The spacecraft will
$(A)$ immediately stop, throwing all of the occupants to the front of the craft. $(B)$ begin slowing down, eventually coming to a rest in the cold emptiness of space. $(C)$ keep moving at constant speed for a while, but then be- gin to slow down. $(D)$ keep moving forever at the same speed.

What are the mass and weight of $(a)$ a $1420$-lb snowmobile and $(b)$ a $412$-kg heat pump?

A space traveler whose mass is $75.0$ kg leaves Earth. Com- pute his weight $(a)$ on Earth, $(b)$ on Mars, where $g=3.72$ m/s$^2$, and $(c)$ in interplanetary space. $(d)$ What is his mass at each of these locations?

The following statement is true; explain it. Two teams are having a tug of war; the team that pushes harder (horizon- tally) against the ground wins.

A large rock $\it{sits}$ on your toe. Which of the concepts is most important in determining how much it hurts? $(A)$ The mass of the rock. $(B)$ The weight of the rock. $(C)$ Both the mass and the weight of the rock are impor- tant. $(D)$ Either the mass or the weight, as the two are related by a single multiplicative constant $g$.

Comment on whether the following pairs of forces are exam- ples of action$–$reaction: $(a)$ The Earth attracts a brick; the brick attracts the Earth. $(b)$ A propellered airplane pushes air toward the tail; the air pushes the plane forward. $(c)$ A horse pulls forward on a cart, moving it; the cart pulls backward on the horse. $(d)$ A horse pulls forward on a cart without moving it; the cart pulls back on the horse. $(e)$ A horse pulls forward on a cart without moving it; the Earth exerts an equal and op- posite force on the cart. $(f)$ The Earth pulls down on the cart; the ground pushes up on the cart with an equal and opposite force.

A large rock $\it{sits}$ on your toe. Which of the concepts is most important in determining how much it hurts? $(A)$ The mass of the rock. $(B)$ The weight of the rock. $(C)$ Both the mass and the weight of the rock are impor- tant. $(D)$ Either the mass or the weight, as the two are related by a single multiplicative constant $g$.

A horse is urged to pull a wagon. The horse refused to try, citing Newton’s third law as a defense: the pull of the horse on the wagon is equal but opposite to the pull of the wagon on the horse. “If I can never exert a greater force on the wagon than it exerts on me, how can I ever start the wagon moving?” asks the horse. How would you reply?

What are the weight in newtons and the mass in kilograms of $(a)$ a $5.00$-lb bag of sugar, $(b)$ a $240$-lb fullback, and $(c)$ a $1.80$-ton car? ($1$ ton $= 2000$ lb.)

Two blocks, with masses $m_1=4.6$ kg and $m_2=3.8$ kg, are connected by a light spring on a horizontal frictionless table. At a certain instant, when $m_2$ has an acceleration $a_2=$ $2.6$ m/s$^2$, $(a)$ what is the force on $m_2$ and $(b)$ what is the accel- eration of $m_1?$