In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. A curler accelerates a stone to a speed of 3.0 m/s over a time of 2 s.
a)How much force does the curler exert on the stone?
b)What average power does the curler use to bring the stone up to speed?
The acceleration rate while pushing is 3.0/2 = 1.5 m/s^2
The force required to accelerate the stone at that rate is F = M*a = 30 N.
This assumes zero ice friction resistance. That is a fairly good assumption, since they travel so far.
Average power = (kinetic energy added)/(2 seconds)
= (M/2)Vfinal^2/Time = 45 watts
a) Well, if we're talking about curling, I have to say that the force exerted by the curler on the stone is probably pretty strong. I mean, have you seen those guys sweeping the ice like their lives depend on it? But in all seriousness, to calculate the force exerted by the curler, we can use Newton's second law: force equals mass times acceleration. In this case, the force would be equal to the mass of the stone (20 kg) multiplied by the acceleration (3.0 m/s²). So, the force exerted by the curler on the stone is 60 Newtons. That's one strong push!
b) As for the average power used by the curler to bring the stone up to speed, we can use the formula: power equals work divided by time. The work done on the stone to accelerate it can be calculated using the formula: work equals force times distance. Since the distance isn't given, let's just assume the curler pushed the stone for a distance of 1 meter. So, the work would be equal to the force (60 N) multiplied by the distance (1 m), which gives us 60 Joules. Now, if the curler took 2 seconds to bring the stone up to speed, we can divide the work (60 J) by the time (2 s) to find the average power. So, the average power used by the curler would be 30 Watts. That's a lot of power, but I wouldn't recommend using it to heat up your hot chocolate in the winter!
To calculate the force exerted by the curler on the stone, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a).
a) Given:
Mass of the stone (m) = 20 kg
Acceleration of the stone (a) = (final velocity - initial velocity) / time
= (3.0 m/s - 0) / 2 s
= 1.5 m/s²
Using the formula F = m * a, we can calculate the force exerted on the stone:
F = 20 kg * 1.5 m/s²
= 30 N
Therefore, the curler exerts a force of 30 N on the stone.
b) To calculate the average power used by the curler to bring the stone up to speed, we can use the formula:
Power (P) = Work (W) / Time (t)
The work done is equal to the change in kinetic energy, which can be calculated using the formula:
Work (W) = 0.5 * m * (v² - u²)
Where:
m = 20 kg (mass of the stone)
v = 3.0 m/s (final velocity)
u = 0 (initial velocity)
W = 0.5 * 20 kg * (3.0 m/s)²
= 0.5 * 20 kg * 9.0 m²/s²
= 0.5 * 180 kg·m²/s²
= 90 J (joules)
Given:
Time (t) = 2 s
Using the formula P = W / t, we can calculate the average power:
P = 90 J / 2 s
= 45 W
Therefore, the average power used by the curler to bring the stone up to speed is 45 watts.
To calculate the force exerted by the curler on the stone, you can use Newton's second law of motion. The formula is:
Force = mass × acceleration
In this case, the mass of the stone is given as 20 kg, and the acceleration is the change in velocity over time. We can calculate the acceleration using the formula:
Acceleration = (final velocity - initial velocity) / time
a) To calculate the force:
1. Substitute the given values into the equation:
Acceleration = (3.0 m/s - 0 m/s) / 2 s
Acceleration = 1.5 m/s^2
2. Apply Newton's second law of motion:
Force = mass × acceleration
Force = 20 kg × 1.5 m/s^2
Force = 30 N
Therefore, the curler exerts a force of 30 Newtons on the stone.
b) To calculate the average power used by the curler:
Power is defined as the work done per unit of time. The formula to calculate power is:
Power = Work / Time
Since the average power is required, we need to calculate the work done first. The work done is given by the equation:
Work = Force × Distance
In this case, we don't have the distance traveled by the stone. However, we can assume that the distance traveled during acceleration is equal to half the product of the initial and final velocities and the time taken. So, the equation becomes:
Work = Force × (initial velocity + final velocity) × time / 2
1. Substitute the given values into the equation:
Work = 30 N × (0 m/s + 3.0 m/s) × 2 s / 2
Work = 30 N × 3.0 m/s × 2 s / 2
Work = 90 Joules
Now, we have the value of work done. To calculate the average power:
2. Substitute the work value and time into the equation:
Power = Work / Time
Power = 90 J / 2 s
Power = 45 Watts
Therefore, the average power used by the curler to bring the stone up to speed is 45 Watts.