A speed skater goes around a turn that has a radius of 35 m. The skater has a speed of 14 m/s and experiences a centripetal force of 460 N. What is the mass of the skater?
Well, well, well, it seems like we have a need for some mass humor!
To find the mass of the skater, we can use the formula for centripetal force. Feeling curious, are you ready for some mathematical comedy?
The centripetal force is given by the equation F = (m * v^2) / r, where F is the force, m is the mass, v is the speed, and r is the radius.
Now let's rearrange the equation to solve for mass. Remember, math jokes are always a plus!
m = (F * r) / v^2
Substituting in the values you provided, we get:
m = (460 N * 35 m) / (14 m/s)^2
Now let's solve this equation and find out the punchline, I mean, the mass of the skater!
*makes sound of calculations*
Drumroll, please...
The mass of the skater is approximately 95.92 kilograms.
I hope I lightened up the equation for you a bit with my clowntastic humor!
To find the mass of the skater, we can use the formula for centripetal force:
F = (m*v^2) / r
where:
F = centripetal force (given as 460 N)
m = mass of the skater (unknown)
v = speed of the skater (given as 14 m/s)
r = radius of the turn (given as 35 m)
Rearranging the formula, we have:
m = (F * r) / v^2
Substituting the given values, we get:
m = (460 N * 35 m) / (14 m/s)^2
m = (16100 N*m) / (196 m^2/s^2)
Now let's evaluate the equation:
m = 16100 N*m / 196 m^2/s^2
m = 82.14 kg
Therefore, the mass of the skater is approximately 82.14 kg.
To find the mass of the skater, we can use the centripetal force formula, which states:
Centripetal Force = (mass × radius × angular velocity²)
In this case, we are given the following information:
Centripetal Force = 460 N
Radius = 35 m
Speed = 14 m/s
First, we need to find the angular velocity using the formula:
Angular Velocity = Speed / Radius
Plugging in the given values:
Angular Velocity = 14 m/s / 35 m
Angular Velocity = 0.4 rad/s (rounded to one decimal place)
Now, substituting the values into the centripetal force formula:
460 N = mass × 35 m × (0.4 rad/s)²
Rearranging the equation to solve for mass:
mass = 460 N / (35 m × (0.4 rad/s)²)
mass = 460 N / (35 m × 0.16 rad²/s²)
mass = 460 N / 0.56 m²/s²
mass ≈ 821.43 kg (rounded to two decimal places)
Therefore, the mass of the skater is approximately 821.43 kg.