Exam 10: Interactions and Potential Energy

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x)= (-2.00 J ∙ m)/x + (4.00 J ∙ m²)/x².Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m.What is the speed of the object when it is located at ?

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m.It coasts down a slope,and then climbs a hill.The top of the hill is at an elevation of 16 m.What is the speed of the car at the top of the hill? Neglect any frictional effects.

A spring-loaded dart gun is used to shoot a dart straight up into the air,and the dart reaches a maximum height of 24 meters above its point of release.The same dart is shot up a second time from the same gun,but this time the spring is compressed only half as far (compared to the first shot).How far up does the dart go this time? (Neglect friction and assume the spring is ideal and massless.)

A potential energy function is given by U(x)= (3.00 J)x + (1.00 J/m²)x³.What is the force function F(x)that is associated with this potential energy function?

A particle experiences a force given by F(x)= α - βx³.Find the potential field U(x)the particle is in.(Assume that the zero of potential energy is located at x = 0.)

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass.The platform drops 6.00 cm before the person comes to rest.What is the spring constant of the spring?

A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure).The external force is removed,and the block is projected with a velocity v₁ = 1.2 m/s upon separation from the spring.The block descends a ramp and has a velocity 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 over this section is 0.28.The velocity of the block is v₃ = 1.4 m/s at C.The block moves on to D,where it stops.The height h of the ramp is closest to

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope and a uniform surface.When the skier reaches the bottom of the hill,her speed is 30.0 m/s. (a)How much work is done by friction as the skier comes down the hill? (b)What is the magnitude of the friction force if the skier travels directly down the hill?

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it from the floor?

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure.What is the length s of the ramp from A to B?

A force on an object is given by F(x)= ( -4.00 N/m)x + ( 2.00 N/m³)x³.What is the change in potential energy in moving from x = 1.00 m to x = 2.00 m?

In the figure,a block of mass m is moving along the horizontal frictionless surface with a speed of 5.70 m/s.If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260,how far does the block travel up the incline?

An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0,as shown in the figure.A very small 4.0-kg ball is attached to the other end of the rod.The ball is held at A,where the rod makes a 30° angle above the horizontal,and is released.The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B.The tension in the rod when the ball passes through the lowest point at D is closest to

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long.You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest.What is your sister's mass,assuming negligible friction?

Swimmers at a water park have a choice of two frictionless water slides as shown in the figure.Although both slides drop over the same height,h,slide 1 is straight while slide 2 is curved,dropping quickly at first and then leveling out.How does the speed v₁ of a swimmer reaching the end of slide 1 compares with v₂,the speed of a swimmer reaching the end of slide 2?