How Many Revolutions per Minute Does the Cart Make?

Question:

If the tension in the rope is 75 N and the student spins the cart and bag around in a circle, keeping the rope parallel to the ground, how many revolutions per minute (rpm) does the cart make?

Answer:

The cart makes approximately 10.5 revolutions per minute (rpm).

To calculate the number of revolutions per minute (rpm) that the cart makes, we can use the formula ω = v / r. Where ω is the angular velocity, v is the linear velocity, and r is the radius of the circular path. The tension in the rope can be expressed as T = m * v^2 / r. Where T is the tension, m is the mass, v is the linear velocity, and r is the radius of the circular path. In this case, the tension is given as 75 N, the mass of the bag and cart is 31 kg (25 kg + 6 kg), and the radius of the circular path is 2 m.

So we have:

75 N = 31 kg * v^2 / 2 m

Now we can solve for v:

v^2 = (75 N * 2 m) / 31 kg = 4.8387 m^2/s^2

v = √(4.8387 m^2/s^2) = 2.2 m/s

Finally, we can calculate the angular velocity:

ω = v / r = 2.2 m/s / 2 m = 1.1 rad/s

To convert the angular velocity to revolutions per minute (rpm), we multiply by (60 s/min) / (2π rad), since there are 2π radians in one revolution:

ω_rpm = (1.1 rad/s) * (60 s/min) / (2π rad) = 10.5 rpm