a weight of 1000g falls freely to a platform from a height of 10 meters. What amount of heat will be evolved when the weight strikes the platform?
23.4 cal
Well, let's see. When it comes to heat, weightlifting isn't usually the first thing that comes to mind. However, in this case we have a falling weight, so let's 'weigh' our options.
If the weight falls freely to a platform from a height of 10 meters, it will definitely make an impact. But as for heat, I'm afraid this situation won't really generate much of that.
The energy from the falling weight will be transferred into potential energy, kinetic energy, and a little bit of sound energy when it hits the platform. However, the amount of heat generated will be minimal. But hey, at least you've got a great fall-guy story for your friends!
To calculate the amount of heat evolved when the weight strikes the platform, we need to use the equation for potential energy:
Potential Energy = mgh
where:
m = mass of the weight (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (in meters)
First, let's convert the weight from grams to kilograms. Since 1 kg = 1000 g, the weight is 1000 g is equal to 1 kg.
Next, we can substitute the values into the equation:
Potential Energy = (1 kg) x (9.8 m/s^2) x (10 m)
Potential Energy = 98 Joules
The amount of heat evolved when the weight strikes the platform will also be equal to 98 Joules.
To calculate the amount of heat evolved when the weight strikes the platform, we need to consider the potential energy and kinetic energy of the weight.
The potential energy (PE) of an object of mass (m) and height (h) is given by the formula:
PE = m * g * h
Where:
m = mass of the object (in kilograms)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (in meters)
In this case, the mass of the weight is given as 1000g, so we need to convert it to kilograms:
mass (m) = 1000g = 1000/1000 kg = 1 kg
The height (h) is given as 10 meters.
Therefore, the potential energy (PE) of the weight is:
PE = 1 kg * 9.8 m/s^2 * 10 m = 98 J
Now, when the weight strikes the platform, it loses its potential energy and gains kinetic energy. The amount of heat evolved is equal to the change in kinetic energy.
The formula for kinetic energy (KE) is:
KE = 1/2 * m * v^2
Where:
m = mass of the object (in kilograms)
v = final velocity (in meters per second)
To calculate the final velocity, we need to use the principle of conservation of energy. The potential energy (PE) lost by the weight is converted into kinetic energy (KE) at the point of impact, so:
PE = KE
Therefore:
1 kg * 9.8 m/s^2 * 10 m = 1/2 * 1 kg * v^2
98 J = 0.5 * v^2
Rearranging the equation to solve for v^2:
v^2 = (98 J) / (0.5 kg)
v^2 = 196 m^2/s^2
Taking the square root:
v ≈ √196 m/s
v ≈ 14 m/s
Now that we have the final velocity, we can calculate the kinetic energy using the formula mentioned earlier:
KE = 0.5 * 1 kg * (14 m/s)^2
KE = 98 J
Therefore, the amount of heat evolved when the weight strikes the platform is 98 Joules.