1)A 150gram ball is thrown at a wall with a speed of 12m/s. If all the kinetic energy is converted to heat energy with 100% efficiency how many joules of heat energy does the wall absorb evrey throw?

E =

 

The amount of energy kinetic energy possessed by the ball is given by the formula above.
E = 0.5 X 0.15 X 12 X 12 = 10.8 joules of heat energy.

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A 100kg cart is released from position "A" with an initial speed of 30m/s.The designer of the roller coaster wants the cart to come to a complete stop at point "B". How high must point "B" be above the ground?

The law of conservation of energy applies. The gravitational potential energy of the cart at point ("A") is given by the expression below.

E =mgh

Step 1 -find the gravitational potential energy the cart has at point "A"

E = 100 X 9.8 X 120 = 117600joules

Step 2 -find the kinetic energy of the cart at position "A"

E =
Kinetic energy = 0.5 X 100 X 30 X 30 = 45000 joules. The total energy of the cart at position "A" is 117600 + 20000 =162600

Step 3- Transform the fomula below to make it equal to "h" and then calculate "h"

E =mgh

162600 / ( 100 X 9.8) = 169.5m

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A cart weighing 80.0 kilograms is released from position "A" on a roller coaster. With what speed will it arrive at position "B" assuming no friction or air resistance?

Step one- The law of conservation of energy applies. All the gravitational potential energy of the cart at position "A" is converted into partially kinetic(moving)energy and gravitational potential energy.

Step two- The gravitational energy stored by the cart at position "A" is calculated by the expression below.

E =mgh
(mass in kilograms,g is the gravitational constant(9.8), h is the height in metres)
Gravitational potential energy of the ball = 80 X 9.8 X 150= 117600 joules.

Step three- When the cart is at position "B" some of the energy is in the form of gravitational potential energy and some in kinetic. The amount of gravitational potential energy at ("B") is given by the expression below

E =mgh

Gravitational potential = 80 X 9.8 X 120 = 117600

Total amount of energy is given by the expression belowv and is equal to the total energy at position "A"..

E (total)= (80 X 9.8 X 120 ) + kinetic energy
=> 117600 -94080 = 23520 = kinetic energy
Transform the kinetic energy formula to make it equal to velocity.

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