Chapter 10: Interactions and Potential Energy

The three balls in FIGURE $Q10.4$, which have equal masses, are fired with equal speeds from the same height above the ground. Rank in order, from largest to smallest, their speeds v_a, v_b, and v_c as they hit the ground. Explain.

a. What is the kinetic energy of a $1500kg$car traveling at a speed of $30m/s(\approx 65mph)$?

b. From what height would the car have to be dropped to have this same amount of kinetic energy just before impact?

A cable with $20.0N$ of tension pulls straight up on a $1.50kg$ block that is initially at rest. What is the block’s speed after being lifted $2.00m$? Solve this problem using work and energy.

A very slippery ice cube slides in a vertical plane around the inside of a smooth, $20-cm$-diameter horizontal pipe. The ice cube’s speed at the bottom of the circle is $3.0m/s$. What is the ice cube’s speed at the top?

A$50g$ice cube can slide up and down a frictionless $30°$slope. At the bottom, a spring with spring constant $25N/m$is compressed $10cm$and used to launch the ice cube up the slope. How high does it go above its starting point?

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a$10-m$-high hill, then descends $15m$ to the track’s lowest point. You’ve determined that the spring can be compressed a maximum of $2.0m$ and that a loaded car will have a maximum mass of $400kg$. For safety reasons, the spring constant should be $10\%$ larger than the minimum needed for the car to just make it over the top.

a. What spring constant should you specify?

b. What is the maximum speed of a$350kg$ car if the spring is compressed the full amount?

It’s been a great day of new, frictionless snow. Julie starts at the top of the $60°$slope shown in $FIGUREP10.44.$At the bottom, a circular arc carries her through a $90°$turn, and she then launches off a $3.0-m$-high ramp. How far horizontally is her touchdown point from the end of the ramp?

A block of mass $m$slides down a frictionless track, then around the inside of a circular loop-the-loop of radius $R$. From what minimum height $h$ must the block start to make it around without falling off? Give your answer as a multiple of $R$.

A$1000kg$safe is $2.0m$above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it $50cm$. What is the spring constant of the spring?

You have a ball of unknown mass, a spring with spring constant $950N/m$, and a meter stick. You use various compressions of the spring to launch the ball vertically, then use the meter stick to measure the ball’s maximum height above the launch point. Your data are as follows:

Use an appropriate graph of the data to determine the ball’s mass.