Mechanics | Relativity Answers

the energy of a particle of mass m bound by a special kind of spring is E=p^2/2m +kx^4 where k is a positive constant .use the heisenbergs uncertainty principle to calculate the minimum possible energy of the particle.

A body starts from rest and accelerates uniformly at a rate of 5m/s2. Calculate its velocity after 90mz

When an egg falls and lands on a carpet will the impulse be less, greater than or the same as the impulse it would have if it lands on a hard floor? Explain.
In which case (carpet or hard floor) is here a larger time of impact? Explain.
In which case (carpet or hard floor) is there a larger force? Explain.
In which case (carpet or hard floor) is there a larger change in momentum? Explain.

A compressed spring is used to propel a ball bearing along a track which contains a circular loop of radius 0.10m in a vertical plane. The spring obeys Hooke's law and requires a force of 0.20N to compress it by 1.0mm.
(a) The spring is compressed by 30 mm. Calculate the energy stored in the spring.
(b) A ball bearing of mass 0.025kg is placed against the end of the spring which is then released. Calculate,
(I) the speed with which the ball bearing least the spring
(ii) the speed of the ball at the top of the loop
(iii) the force exerted on the ball by the track at the top of the loop
Assume that the effects of friction can be ignored.

Calculate the force necessary to keep a mass 0.2kg moving in a horizontal circle of radius 0.5m with a period of 0.5s. What is the direction of the force?

A racing car of 1000kg moves round a banked track at a constant speed of 108kmh^-1. Assuming the total reaction at the wheels is normal to the track, and the horizontal radius of the track is 100m, calculate the angle of inclination of the track to the horizontal and the reaction of the wheels.

A truck accelerates from rest directly towards a car leaving a parking garage. The car has a constant velocity of 25m/s towards the truck. The truck accelerates towards the car from 100m away. The collision takes 2.86 seconds to occur. The truck has a constant rate of acceleration.
A) draw separate motion diagrams for each vehicle. Be sure to include all known and unknown variables. B) What is the final velocity of the truck when it collides with the car?

An inquisitive physics student and mountain climber climbs a 50m cliff that overhangs a calm pool of water. He throws two stones vertically downwards 1s apart and observes that they cause a single splash. The first stone has an initial velocity of 2ms^-1.
(a) At what time after release of the first stone will the two stones hit the water?
(b) What is the initial velocity that the second stone should have if they are to hit simultaneously?
(c) What will the velocity of each stone be at the instant they hit the water?

A falling object requires 1.50s to travel the last 30m before hitting the ground. From what height above the ground did it fall?

Power supplied to a particle of mass 2kg varies with time as P = 3t^2 /2 .Here t is in second.If the velocity of the particle at t=0 is v=0.The velocity of the particle at the time t=2 s will be?