BackA horizontal spring with spring constant 85 N/m extends outward from a wall just above floor level. A 1.5 kg box sliding across a frictionless floor hits the end of the spring and compresses it 6.5 cm before the spring expands and shoots the box back out. How fast was the box going when it hit the spring?
Stretchable ropes are used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length ℓ is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height ℓ above the anchor point, he slips and falls under the force of gravity for a distance 2ℓ, after which the rope becomes taut and stretches a distance x as it stops the climber (see Fig. 7–37). Assume a stretchy rope behaves as a spring with spring constant k. Applying the work-energy principle, show that .
In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. What is of 1.0 kg of water?
(II) At an accident scene on a level road, investigators measure a car’s skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30. What is wrong with a car that skids (see page 131)?
A 2.0 kg particle moving along the x-axis experiences the force shown in FIGURE EX9.22. The particle's velocity is 3.0 m/s at x = 0 m. At what point on the x-axis does the particle have a turning point?
The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m. How much work is done by gravity?
You throw a -N rock vertically into the air from ground level. You observe that when it is m above the ground, it is traveling at m/s upward. Use the work–energy theorem to find the rock's speed just as it left the ground.
A box slides across the floor with an initial speed of 3.5m/s. If the coefficient of kinetic friction is 0.15, how far will the box slide before stopping completely?
A 737-800 jet airliner has twin engines, each with 105 kN thrust. A 78,000 kg jet reaches a takeoff speed of 70 m/s in a distance of 1100 m. What is the increase in thermal energy due to rolling friction and air drag?
Stretchable ropes are used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length ℓ is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height ℓ above the anchor point, he slips and falls under the force of gravity for a distance 2ℓ, after which the rope becomes taut and stretches a distance x as it stops the climber (see Fig. 7–37). Assume a stretchy rope behaves as a spring with spring constant k. Assuming m = 85kg, ℓ = 8.0 m and, k = 850 N/m determine x/ℓ (the fractional stretch of the rope) and kx / mg (the force that the rope exerts on the climber compared to his own weight) at the moment the climber’s fall has been stopped.
A system of two objects has and . How much work is done by interaction forces?
In the game of paintball, players use guns powered by pressurized gas to propel 33-g gel capsules filled with paint at the opposing team. Game rules dictate that a paintball cannot leave the barrel of a gun with a speed greater than 85 m/s. Model the shot by assuming the pressurized gas applies a constant force F to a 33-g capsule over the length of the 32-cm barrel. Determine F by using the work-energy principle.
A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the block's speed after being lifted 2.00 m? Solve this problem using work and energy.