A speed skater goes around a turn that has a radius of 29 m. The skater has a speed of 14 m/s and experiences a centripetal force of 450 N. What is the mass of the skater?
450 = m*v^2 / r
where m is mass, v is speed, and r is radius
A 0.0371 kg ball is shot from the plunger of a pinball machine. Because of a centripetal force of 0.0491 N, the ball follows a circular arc whose radius is 0.101 m. What is the speed of the ball?
To find the mass of the skater, we can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the skater
v is the speed of the skater
r is the radius of the turn
Plugging in the given values:
450 N = (m * (14 m/s)^2) / 29 m
Now we can solve for the mass (m). First, let's simplify the equation:
450 N * 29 m = m * (14 m/s)^2
13,050 N*m = m * 196 m^2/s^2
Divide both sides of the equation by 196 m^2/s^2:
13,050 N*m / 196 m^2/s^2 = m
66.6 kg ≈ m
Therefore, the mass of the skater is approximately 66.6 kg.
To find the mass of the skater, we can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F = Centripetal force (450 N)
m = Mass of the skater (to be determined)
v = Speed of the skater (14 m/s)
r = Radius of the turn (29 m)
Rearranging the formula, we can solve for the mass (m):
m = (F * r) / v^2
Substituting the given values:
m = (450 N * 29 m) / (14 m/s)^2
m = (13,050 N·m) / 196 m^2/s^2
m ≈ 66.6 kg
Therefore, the mass of the skater is approximately 66.6 kg.