The speed of a hockey puck (mass=100.0 g) decreases from 45.00 m/s to 42.68 m/s in coasting 16.00 m across the ice.
a) How much thermal energy was produced?
b) What frictional force was acting on the puck?
To calculate the thermal energy produced and the frictional force acting on the puck, we can use the work-energy principle and Newton's second law of motion.
a) To calculate the thermal energy produced, we need to determine the change in kinetic energy of the puck. We can use the equation:
ΔKE = 1/2 * m * (vf^2 - vi^2)
where ΔKE is the change in kinetic energy, m is the mass of the puck, vf is the final velocity, and vi is the initial velocity.
Plugging in the given values:
m = 100.0 g = 0.1 kg
vf = 42.68 m/s
vi = 45.00 m/s
ΔKE = 1/2 * 0.1 * (42.68^2 - 45.00^2)
Calculating ΔKE will give us the thermal energy produced.
b) To calculate the frictional force acting on the puck, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Fnet = m * a
In this case, the net force is the frictional force acting on the puck. The acceleration can be calculated using the equation:
a = (vf - vi) / t
where t is the time taken to traverse the distance.
Given that the distance is 16.00 m, we can calculate the time taken using the equation:
t = d / v
where d is the distance and v is the average velocity during the coasting period. The average velocity can be calculated using:
v = (vf + vi) / 2
Plugging in the given values, we can calculate the time taken and then use it to calculate the frictional force using Newton's second law.
Note: We assume that the effects of any other forces (such as air resistance) are negligible in this scenario.
Once we have ΔKE (which represents the thermal energy produced) and the frictional force, we can provide answers to both sub-questions. Let me know if you would like the specific calculations.