Exam 7: Work and Energy

As shown in the figure,a 1.45-kg block is held in place against the spring by a 21-N horizontal external force.The external force is removed,and the block is projected with a velocity $v 1 = 1.2 \mathrm {~m} / \mathrm { s }$ as it separates from the spring.The block descends a ramp and has a velocity $v _ { 2 } = 2.1 \mathrm {~m} / \mathrm { s }$ at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction between the block and the rough surface is 0.29.The velocity of the block is $v _ { 3 } = 1.4 \mathrm {~m} / \mathrm { s }$ at C.The block moves on to D,where it stops.How much of the mechanical energy was converted to internal energy between points B and C?

A 0.12-kg block is held in place against the spring by a 35-N horizontal external force.The external force is removed,and the block is projected with a velocity $v 1 = 1.2 \mathrm {~m} / \mathrm { s }$ when it separates from the spring,as shown in the figure.The block descends a ramp and has a velocity $v _ { 2 } = 1.4 \mathrm {~m} / \mathrm { s }$ at the bottom of the ramp.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction between the block and the rough surface is 0.26.The block moves on to D,where it stops.By how many centimeters was the spring initially compressed?

Two simple pendulums of equal length l = 0.45 m are suspended from the same point.The pendulum bobs are small solid steel spheres.The first bob is drawn back to make a 35° angle with the vertical,while the other one is left hanging at rest.If the first bob has a mass of 0.25 kg and the second has a mass of $0.54 \mathrm {~kg} \text {, }$ how high will the second bob rise above its initial position when struck elastically by the first bob after it is released?

If the force exerted on an object is in the negative direction,the work it does on the object must be

In a perfectly elastic collision,a 400-g ball moving toward the east at 3.7 m/s suddenly collides head-on with a 200 g ball sitting at rest. (a)Determine the velocity of the first ball just after the collision. (b)Determine the velocity of the second ball just after the collision. (c)Is kinetic energy conserved in this collision? How do you know?

Rita raises a 10kg package to a height of 2.5 m in 2.0 s. (a)How much work did she do on the package? (b)How much power was expended on the package? (c)If she were to raise the package in 1.0 s rather than 2.0 s,how do the work and power change?

A block of mass m = 9.0 kg and speed V and is behind a block of mass M = 27 kg and speed of $0.50 \mathrm {~m} / \mathrm { s }$ as shown int the figure.The surface is frictionless,and the blocks suddenly collide and couple.After the collision,the blocks have a common speed of 0.90 m/s.How much kinetic energy of the blocks is lost due to the collision?

A 320-g air track cart traveling at 1.25 m/s suddenly collides elastically with a stationary 270-g cart.What is the speed of the 320-g cart just after the collision?

The figure shows two crates,each of mass m = 24 kg,that are connected by a very light wire.The coefficient of kinetic friction between the crate on the inclined surface and the surface itself is 0.31.Find the speed of the crates after they have moved 1.6 m starting from rest.

An object initially at rest suddenly explodes in two fragments of masses $2.6 \mathrm {~kg}$ and $3.3 \mathrm {~kg}$ that move in opposite directions.If the speed of the first fragment is $3.6 \mathrm {~m} / \mathrm { s }$ find the internal energy of the explosion.

An ideal spring with a spring constant of 15 N/m is initially compressed by 3.0 cm from its uncompressed position.How much work is required to compress the spring an additional 4.0 cm?

A stone is released from rest at a height h at the left side of a loop-the-loop,as shown in the figure.There is no appreciable friction force exerted by the track or by air resistance.If the radius of the loop is R,what is the minimum height h for which the stone will not fall off the track at the top of the loop?

You carry a 7.0-kg bag of groceries $1.2 \mathrm {~m}$ above the ground at constant speed across a $2.7 \mathrm {~m}$ room.How much work do you do on the bag in the process?

A certain car traveling at 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied.In approximately what distance would the car have stopped had it been going 105.4 mph?

When you throw a pebble straight up with initial speed V,it reaches a maximum height H assuming there is no air resistance.At what speed should you throw it up vertically so it will go twice as high?

Suppose you left five 100-W light bulbs burning in the basement for two weeks.If electricity costs 10.0¢/kW∙h,(a)how much did the electricity cost (to the nearest dollar)to leave those bulbs on,and (b)how many joules of electrical energy did they consume?

An object hits a wall and bounces back with half of its original speed.What is the ratio of the final kinetic energy to the initial kinetic energy of the object?

What is the net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds?

If the units of your answer are kg ∙ m²/s³,which of the following types of quantities could your answer be? (There could be more than one correct choice.)

A baseball pitcher is employing a ballistic pendulum to determine the speed of his fastball.A $3.3 - \mathrm { kg }$ lump of clay is suspended from a cord 2.0 m long.When the pitcher throws his fastball aimed directly at the clay,the ball suddenly becomes embedded in the clay and the two swing up to a maximum height of 0.080 m.If the mass of the baseball is 0.21 kg,find the speed of the pitched ball.