1. Determine the specific heat of a certain metal if a 450-g sample of it loses 34,500 joules of heat as its temperature drops by 97degC.
2. The temperature of a 55-g sample of a certain metal drops by 113degC as it losses 3,500 J of heat. What is the specific heat of the metal?
3. A golfer wishes to hit his drives further by increasing the kinetic energy of the golf club when it strikes the ball. Which would have the greater effect on the energy transferred to the ball by the driver – doubling the mass of the club or doubling the speed of the club head? Explain.
4. A stone is dropped from a certain height and penetrates into the mud. All else being equal, if it is dropped from twice the height, how much farther should it penetrate?
1. To determine the specific heat of a certain metal, we can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of heat transferred
m is the mass of the metal
c is the specific heat of the metal
ΔT is the change in temperature
In this case, we are given:
m = 450 g
Q = -34,500 J (negative because the metal is losing heat)
ΔT = -97°C (negative because the temperature is dropping)
Plugging in these values into the formula, we get:
-34,500 J = 450 g * c * (-97°C)
Simplifying the equation, we get:
c = -34,500 J / (450 g * -97°C)
Calculating this, we find the specific heat of the metal.
2. Similar to the previous question, to determine the specific heat of a metal when given the change in temperature and heat transferred, we use the same formula:
Q = m * c * ΔT
We are given:
m = 55 g
Q = -3,500 J (again, negative because the metal is losing heat)
ΔT = -113°C
Plugging in these values, we have:
-3,500 J = 55 g * c * (-113°C)
Simplifying the equation, we get:
c = -3,500 J / (55 g * -113°C)
Calculating this, we can find the specific heat of the metal.
3. To determine the greater effect on the energy transferred to the ball by the driver, we need to consider the equation for kinetic energy:
KE = 0.5 * m * v^2
Where:
KE is the kinetic energy
m is the mass
v is the velocity/speed
If we double the mass of the club, we can see that the kinetic energy will increase since it's directly proportional to the mass. However, if we double the speed of the club head, the kinetic energy will increase even more since it's proportional to the square of the velocity. Therefore, doubling the speed of the club head will have a greater effect on the energy transferred to the ball.
4. The distance penetrated by the stone when dropped from a certain height depends on the potential energy it initially has, which is determined by its height. All else being equal, if the stone is dropped from twice the height, it will have twice the potential energy at the start. As it falls and penetrates into the mud, this potential energy is gradually converted into kinetic energy, which determines how far it penetrates. Therefore, if the stone is dropped from twice the height, it should penetrate farther because it has more potential energy to convert into kinetic energy.