Problem 48
An ingenious bricklayer builds a device for shooting bricks up to the top of the wall where he is working. He places a brick on a vertical compressed spring with force constant \(k = 450\) N/m and negligible mass. When the spring is released, the brick is propelled upward. If the brick has mass 1.80 kg and is to reach a maximum height of 3.6 m above its initial position on the compressed spring, what distance must the bricklayer compress the spring initially? (The brick loses contact with the spring when the spring returns to its uncompressed length. Why?)
Problem 49
A force in the \(+x\)-direction with magnitude \(F(x) = 18.0 \, \mathrm{N} - (0.530 \, \mathrm{N/m})x\) is applied to a 6.00-kg box that is sitting on the horizontal, frictionless surface of a frozen lake. \(F(x)\) is the only horizontal force on the box. If the box is initially at rest at \(x = 0\), what is its speed after it has traveled 14.0 m?
Problem 50
A crate on a motorized cart starts from rest and moves with a constant eastward acceleration of \(a = 2.80 \, \mathrm{m/s}^2\). A worker assists the cart by pushing on the crate with a force that is eastward and has magnitude that depends on time according to \(F(t) = (5.40 \, \mathrm{N/s})t\). What is the instantaneous power supplied by this force at \(t = 5.00\) s?
Problem 51
How many joules of energy does a 100-watt light bulb use per hour? How fast would a 70 kg person have to run to have that amount of kinetic energy?
Problem 52
It is 5.0 km from your home to the physics lab. As part of your physical fitness program, you could run that distance at 10 km/h (which uses up energy at the rate of 700 W), or you could walk it leisurely at 3.0 km/h (which uses energy at 290 W). Which choice would burn up more energy, and how much energy (in joules) would it burn? Why does the more intense exercise burn up less energy than the less intense exercise?
Problem 53
On December 27, 2004, astronomers observed the greatest flash of light ever recorded from outside the solar system. It came from the highly magnetic neutron star SGR 1806-20 (a \(magnetar\)). During 0.20 s, this star released as much energy as our sun does in 250,000 years. If \(P\) is the average power output of our sun, what was the average power output (in terms of \(P\)) of this magnetar?
Problem 54
A 20.0-kg rock is sliding on a rough, horizontal surface at 8.00 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.200. What average power is produced by friction as the rock stops?
Problem 55
A tandem (two-person) bicycle team must overcome a force of 165 N to maintain a speed of 9.00 m/s. Find the power required per rider, assuming that each contributes equally. Express your answer in watts and in horsepower.
Problem 56
When its 75-kW (100-hp) engine is generating full power, a small single-engine airplane with mass 700 kg gains altitude at a rate of 2.5 m/s (150 m/min, or 500 ft/min). What fraction of the engine power is being used to make the airplane climb? (The remainder is used to overcome the effects of air resistance and of inefficiencies in the propeller and engine.)
Problem 57
Your job is to lift 30-kg crates a vertical distance of 0.90 m from the ground onto the bed of a truck. How many crates would you have to load onto the truck in 1 minute (a) for the average power output you use to lift the crates to equal 0.50 hp; (b) for an average power output of 100 W?
