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Physics problems: conservation laws

Part 2

 

Problem 11.

At an amusement park there is a roller coaster ride ("ride of Steel"). After the first drop, riders are moving at the speed of 120 km/h, entering an underground tunnel. Given the fact that the roller coaster was moving at a speed of 4 km/h at the top of the hill, determine the vertical drop that these participants fell through. Neglect friction.

Solution

 

Problem 12.

A man drops a 10 kg rock from the top of a ladder of height 5 m.

What is its speed just before it hits the ground?

What is its Kinetic Energy when it reaches the ground?

Solution

 

Problem 13.

A cyclist intends to cycle up a 8 degrees hill whose vertical height is 150 m. If each complete revolution of the pedals moves the bike 6 m   along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 30 cm. The total mass of the cyclist and his bike is 100 kg.

Solution

 

Problem 14.

A body of mass 5 kg slides a distance of 6 m down a rough Inclined plane 30 degree. Then it moves on frictionless horizontal surface and compresses a spring. The coefficient of kinetic friction is 0.1 and the spring constant is 300 N/m. Find the maximum compression of the spring.

Solution

 

 

 

Problem 15.

A particle of mass m moving in a circular orbit of radius r has angular momentum j about its center. Calculate kinetic energy in terms of j, m and r.

Solution

 

Problem 16.

A stone was at free fall from a 400 meters building. Before reaching the ground, if the stone was at a height of 360 meters, what is the kinetic energy of the stone at the height? The mass of the stone is 10 kg.

Solution

 

Problem 17.

Calculate the displacement to amplitude ratio for simple harmonic motion when kinetic energy is 90% of the total energy.

Solution

 

Problem 18.

A bullet travelling horizontally losses 1/20 th of its velocity while penetrating a wooden plank, how many such planks are required to stop the bullet.

Solution

 

Problem 19.

If a body losses half of its velocity on penetrating 3cm in a wooden block then how much will it penetrate more before coming to rest.

Solution

 

Problem 20.

Two bodies of mass M and 4M are moving with equal kinetic energy. What is the ratio of their linear momenta?

Solution

 

 

 

 

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