Chapter 6: Dynamics I: Motion Along a Line

A $65$kg gymnast wedges himself between two closely spaced vertical walls by pressing his hands and feet against the walls. What is the magnitude of the friction force on each hand and foot? Assume they are all equal.

A baggage handler drops your $10$kg suitcase onto a conveyor belt running at$2.0$ m/s. The materials are such that ${\mu }_s=0.50$ and . How far is your suitcase dragged before it is riding smoothly on the belt?

A $2.0$kg wood block is launched up a wooden ramp that is inclined at a $30°$angle. The block’s initial speed is $10$m/s.

a. What vertical height does the block reach above its starting point?

b. What speed does it have when it slides back down to its starting point?

It’s a snowy day and you’re pulling a friend along a level road on a sled. You’ve both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. You’ve been walking at a steady $1.5$m/s, and the rope pulls up on the sled at a $30°$angle. You estimate that the mass of the sled, with your friend on it, is $60$kg and that you’re pulling with a force of $75$N. What answer will you give?

A large box of mass $M$is pulled across a horizontal, frictionless surface by a horizontal rope with tension $T$. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are ${\mu }_s$and ${\mu }_k$, respectively. Find an expression for the maximum tension $T_{max}$for which the small box rides on top of the large box without slipping.

A large box of mass $M$is moving on a horizontal surface at speed $V$0 . A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are ${\mu }_s$and ${\mu }_1$, respectively. Find an expression for the shortest distance$d_{min}$ in which the large box can stop without the small box slipping.

You're driving along at$25m/s$with your aunt's valuable antiques in the back of your pickup truck when suddenly you see a giant hole in the road $55$ ahead of you. Fortunately, your foot is right beside the brake and your reaction time is zero!

a. Can you stop the truck before it falls into the hole?

b. If your answer to part a is yes, can you stop without the antiques sliding and being damaged? Their coefficients of friction are ${\mu }_{\mathrm{s}}=0.60$and${\mu }_{\mathrm{k}}=0.30$.

The ${\mu }_{\mathrm{k}}=0.30$wood box in FIGURE $P6.56$slides down a vertical wood wall while you push on it at a $2.0\mathrm{kg}$angle. What magnitude of force should you apply to cause the box to slide down at a constant speed?

FIGURE $P6.56$

A $1.0\mathrm{kg}$wood block is pressed against a vertical wood wall by the$12\mathrm{N}$force shown in $FIGUREP6.57$. If the block is initially at rest, will it move upward, move downward, or stay at rest?

A person with compromised pinch strength in his fingers can exert a force of only$6.0\mathrm{N}$to either side of a pinched object, such as the book shown in FIGURE $P6.58$. What is the heaviest book he can hold vertically before it slips out of his fingers? The coefficient of static friction between his fingers and the book cover is $0.80$.

FIGURE P6.58