Question

a 25 kg bag of sand rests on a 6 kg cart, to which a 2.0-m-long rope is attached. a student holds the other end of the rope and spins the cart and bag around in a circle, keeping the rope parallel to the ground. if the tension in the rope is 75 n, how many revolutions per minute (rpm) does the cart make? ignore all frictions

Answer 1

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

Step-by-step explanation:

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