You decide to pull a \(150 \mathrm{~kg}\) sled across an icy pond that is \(24 \mathrm{~m}\) across. You start pulling with a constant force of \(200 \mathrm{~N}\text{.}\) When you get halfway across the pond, you hear the ice cracking and decide to increase your force so that it increases linearly with distance, eventually reaching \(500 \mathrm{~N}\) when you get to the other side of the pond. How fast is the sled moving when you reach the other side?
As a \(1.4 \times 10^4 \mathrm{~kg}\) jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant \(6.5 \times 10^4 \mathrm{~N/m}\text{.}\) If the spring stretches \(29 \mathrm{~m}\) to stop the plane, what was the plane’s landing speed?
SubsectionExplanation Practice
Explanation8.13.3.Stopping a Meteor I.
You are an astronaut in charge of defending a space station from a small, incoming meteor. The meteor has mass m and speed v, is initially a distance d from the space station, and is moving directly at the space station. Your space station can exert a constant force on the meteor. What force must you exert if you are to stop the meteor before it hits the space station?
Explanation8.13.4.Stopping a Meteor II.
After you save the space station from the meteor, you detect two new incoming meteors: both meteors have the same mass and start the same distance away from the space station. Once again, you are able to stop both meteors right before they hit the space station, but only by setting your space station to exert a force on Meteor 2 that is twice as large as the force on Meteor 1. Based on this, was the initial speed of Meteor 2 greater than, less than, or equal to the initial speed of Meteor 1?
Explanation8.13.5.Three Catapults.
Three catapults are configured to throw the same bowling ball into the air with the same initial speed. Each catapult is positioned at the top of the same tall cliff, but they are designed to release the bowling ball differently.
Catapult A releases the bowling ball at a 30\(^{\circ}\) angle with respect to the horizontal.
Catapult B releases the bowling ball at a 45\(^{\circ}\) angle with respect to the horizontal.
Catapult C releases the bowling ball at a 0\(^{\circ}\) angle with respect to the horizontal.
Rank the three bowling balls by final speed (when the ball hits the ground).
SubsectionNumerical Practice
Calculation8.13.6.Scanning a can.
How much work, in joules, does a supermarket checkout attendant do on a can of soup that he pushes \(0.6 \mathrm{~m}\) horizontally while exerting a force of \(5 \mathrm{~N}\text{?}\)
A car’s bumper is designed to withstand a \(4 \mathrm{~km/hr}\) (\(1.1 \mathrm{~m/s}\)) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses \(0.2 \mathrm{~m}\) while bringing a \(900 \mathrm{~kg}\) car to rest from an initial speed of \(1.1 \mathrm{~m/s}\text{.}\)
Settlers on the surface of a distant planet are trying to determine the local value of g. They throw a wrench downward from a height of \(3 \mathrm{~m}\) with an initial speed of \(2 \mathrm{~m/s}\text{;}\) its speed just before impact is \(10 \mathrm{~m/s}\text{.}\) Use an energy analysis to calculate the local value of \(g\text{.}\)
A rocket sled driver is attempting to break the land speed record out in a flat, dry lake bed. The sled’s thrusters apply a \(20,000 \mathrm{~N}\) force for \(1000 \mathrm{~m}\text{.}\) There is a constant \(4,000 \mathrm{~N}\) wind force directed against the motion of the sled but downward at angle of 30° from the horizontal. If the sled reaches a top speed of \(300 \mathrm{~m/s}\text{,}\) what is its mass? Some large, simplifying assumptions to use here: Ignore friction from the ground, and assume both the wind force and sled mass are constant.
A \(1.8 \mathrm{~kg}\) block slides on a rough, level surface. When it is traveling at \(2 \mathrm{~m/s}\text{,}\) the block hits a linear, ideal spring and compresses it by a distance of \(11 \mathrm{~cm}\) before (momentarily) coming to rest. The coefficient of kinetic friction between the block and the surface is \(0.56\text{.}\) What is the force constant of the spring?
