When the 5 -kg box reaches point A it has a speed $v_{A}=10$ m/s. Determine how high the box reaches up the surface before it comes to a stop. Also, what is the resultant normal force on the surface at this point and the acceleration? Neglect friction and the size of the box.

A $1.5\ \mathrm{kg}$ object moves up the y-axis at a constant speed . When it reaches the origin, the forces $F_1 = 5.0\ \mathrm{N}$ at $37^\circ$ above the +x -axis, $F_2 = 2.5\ \mathrm{N}$ in the +x -direction , $F_3 = 3.5\ \mathrm{N}$ at $45^\circ$ below the - x-axis, and $F_4 = 1.5\ \mathrm{N}$ in the -y -direction are applied to it. (a) Will the object continue to move along the y-axis? (b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?

A luggage handler pulls a $20.0$-$\mathrm{kg}$ suitcase up a ramp in- clined at $32.0\degree$ above the horizontal by a force $\vec{F}$ of magnitude $160 \mathrm{~N}$ that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is $\mu_{\mathrm{k}}=0.300$. If the suitcase travels $3.80$ m along the ramp, calculate (f) If the speed of the suit- case is zero at the bottom of the ramp, what is its speed after it has traveled $3.80$ m along the ramp?

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of $50 \mathrm { N } \cdot \mathrm { m }$. How long does it take the flywheel to reach top angular speed of 1200 rpm?

A resort uses a rope to pull a 55-kg skier up a $40 ^ { \circ }$ slope at constant speed for 100 m. (a) Calculate the tension in the rope if the coefficient of kinetic friction between snow and skis is $\mu _ { k } = 0.20$. (b) How much work does the rope do on the skier?

A double speed trap is set up on a freeway. One police cruiser is hidden behind a billboard, and another is some distance away under a bridge. As a sedan passes by the first cruiser, its speed is measured as $105.9 \mathrm{mph}$. Since the driver has a radar detector, he is alerted to the fact that his speed has been measured, and he tries to slow his car down gradually without stepping on the brakes and alerting the police that he knew he was going too fast. Just taking the foot off the gas leads to a constant deceleration. Exactly $7.05 \mathrm{~s}$ later, the sedan passes the second police cruiser. Now its speed is measured as only $67.1 \mathrm{mph}$, just below the local freeway speed limit. A double speed trap is set up on a freeway. One police cruiser is hidden behind a billboard, and another is some distance away under a bridge. As a sedan passes by the first cruiser, its speed is measured as $105.9 \mathrm{mph}$. Since the driver has a radar detector, he is alerted to the fact that his speed has been measured, and he tries to slow his car down gradually without stepping on the brakes and alerting the police that he knew he was going too fast. Just taking the foot off the gas leads to a constant deceleration. Exactly $7.05 \mathrm{~s}$ later, the sedan passes the second police cruiser. Now its speed is measured as only $67.1 \mathrm{mph}$, just below the local freeway speed limit. b) How far apart are the two cruisers?

A projectile is fired up an incline (incline angle $\phi$ ) with an initial speed $v_i$ at an angle $\theta_i$ with respect to the horizontal $\left(\theta_i>\phi\right)$, as shown in Figure P4.50. (a) Show that the projectile travels a distance $d$ up the incline, where

$$d=\frac{2 v_i^2 \cos \theta_i \sin \left(\theta_i-\phi\right)}{g \cos ^2 \phi}$$

(b) For what value of $\theta_i$ is $d$ a maximum, and what is that maximum value?

A rope of length $L$ and mass $M$ hangs vertically from a ceiling. The tension in the rope is only that due to its own weight. Suppose a wave starts near the bottom of the rope and propagates upward. Does the speed of the wave increase, decrease, or stay the same as it moves up the rope? Explain.

A policeman starts giving chase 60 seconds after a stolen car zooms by at 108 km/hr. At what minimum speed should he drive if he has to catch up with the driver before he manages to get onto an expressway 60 km away?

At its slowest speed, a machine can produce 160 widgets per hour with a 97% efficiency rate ( 2% are defective). For each step up in speed, the machine can produce 10 more widgets per hour, but the percentage of defective widgets increases by $0.8$. Suppose the speed is raised $x$ steps.

a. Write a formula for $n$, where $n(x)$ is the total number of widgets produced hourly.

b. Write a formula for the efficiency rate $e(x)$.

c. Let $w(x)$ be the number of non-defective widgets produced per hour. How are $w$, $n$, and $e$ related?

d. Write a formula for $w(x)$ in terms of $x$.

A double speed trap is set up on a freeway. One police cruiser is hidden behind a billboard, and another is some distance away under a bridge. As a sedan passes by the first cruiser, its speed is measured as $105.9 \mathrm{mph}$. Since the driver has a radar detector, he is alerted to the fact that his speed has been measured, and he tries to slow his car down gradually without stepping on the brakes and alerting the police that he knew he was going too fast. Just taking the foot off the gas leads to a constant deceleration. Exactly $7.05 \mathrm{~s}$ later, the sedan passes the second police cruiser. Now its speed is measured as only $67.1 \mathrm{mph}$, just below the local freeway speed limit. a) What is the value of the deceleration?

What force keeps the Moon up in orbit around the Earth?
(a) No force. The Moon is constantly failing as it orbits the Earth at high speed.
(b) Centrifugal force.
(c ) Centripetal force.
(d) The combined effects of centrifugal force and gravity.
(e) The Earth’s gravity combined with its magnetic field.

An athlete throws a basketball upward from the ground, giving it speed $10.6 \mathrm{~m} / \mathrm{s}$ at an angle of $55.0^{\circ}$ above the horizontal. (a) What is the acceleration of the basketball at the highest point in its trajectory? (b) On its way down, the basketball hits the rim of the basket, $3.05 \mathrm{~m}$ above the floor. It bounces straight up with one-half the speed with which it hit the rim. What height above the floor does the basketball reach on this bounce?

A gyroscope flywheel of radius $2.83 \text{~cm}$ is accelerated from rest at $14.2\text{~ rad/s}^2$ until its angular speed is $2760\text{~ rev/min}$. What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process?