A 17.0 kg child travels down a playground slide 3.50 m high and reaches the bottom with a speed of 2.50 m/s. How much heat was generated due to friction as a result of this process?
my teacher hadn't taught anything about heat..but he did give us this question, thus, i got no idea with this question. please help. thanks a lot.
The heat generated equals the amount of (kinetic + potential) energy lost. That is because of the law of conservation of energy.
In this case, M g H = 17x9.8x3.5 = 583.1 J of potential energy is lost while the kinetic energy increases by (1/2)x(17)x(2.5)^2 = 53.1 J. The rest of the potential energy loss, 530 J, is converted to heat
To solve this problem, we need to understand the concepts of potential energy, kinetic energy, and the law of conservation of energy.
Potential energy refers to the stored energy an object has based on its position. In this case, the child has potential energy due to being at a height of 3.50 m above the ground. The formula for potential energy is given by P.E. = mgh, where m = mass, g = acceleration due to gravity (approximately 9.8 m/s^2), and h = height.
Kinetic energy, on the other hand, refers to the energy an object possesses due to its motion. The formula for kinetic energy is given by K.E. = (1/2)mv^2, where m = mass and v = velocity.
According to the law of conservation of energy, energy cannot be created or destroyed; it can only be converted from one form to another. In this case, the potential energy lost by the child as they slide down the slide will be converted to kinetic energy and heat energy due to friction.
To calculate the potential energy lost, we can use the formula for potential energy:
P.E. = mgh
Substituting the given values:
m = 17.0 kg (mass of the child)
g = 9.8 m/s^2 (acceleration due to gravity)
h = 3.50 m (height of the slide)
P.E. = 17.0 kg × 9.8 m/s^2 × 3.50 m
Calculating this, we find that the potential energy lost is 583.1 J.
Next, we calculate the kinetic energy gained by the child as they reach the bottom of the slide. Using the formula for kinetic energy:
K.E. = (1/2)mv^2
Substituting the given values:
m = 17.0 kg (mass of the child)
v = 2.50 m/s (velocity at the bottom of the slide)
K.E. = (1/2) × 17.0 kg × (2.50 m/s)^2
Calculating this, we find that the kinetic energy gained is 53.1 J.
Now, we can determine the amount of heat generated due to friction. This can be found by subtracting the kinetic energy gained from the potential energy lost:
Heat Generated = Potential Energy Lost - Kinetic Energy Gained
= 583.1 J - 53.1 J
= 530 J
Therefore, the amount of heat generated due to friction in this process is 530 J.