Father and Child Cart Spin: Calculating Rope Tension

Click For Summary
SUMMARY

The discussion focuses on calculating the rope tension required for a father to spin his 24 kg child on a 5.7 kg cart using a 2.0-meter-long rope at 17 RPM on a conical hill with a 24-degree incline. The tension formula T = mv²/R is utilized, with the velocity calculated as 3.6 m/s after converting RPM to radians per second. Participants emphasize the need to analyze both horizontal and vertical components of tension and apply Newton's second law to derive the correct tension value.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with Newton's second law of motion
  • Knowledge of converting RPM to radians per second
  • Basic principles of forces acting on inclined planes
NEXT STEPS
  • Study the derivation of tension in circular motion scenarios
  • Learn about the effects of incline angles on tension calculations
  • Explore advanced applications of Newton's second law in rotational dynamics
  • Investigate the relationship between angular velocity and linear velocity in circular motion
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of circular motion and tension calculations in inclined scenarios.

dubsydub14
Messages
2
Reaction score
0
An energetic father stands at the summit of a conical hill as he spins his 24 kg child around on a 5.7 kg cart with a 2.0-m-long rope. The sides of the hill are inclined at 24 degrees . He keeps the rope parallel to the ground, and friction is negligible
What rope tension will allow the cart to spin with the 17 rpm?

I know the equation for tension is T= mv^2/R

I tried to convert 17 rpms into rad/s and got 1.8 rad/s I got the velocity as 3.6 m/s. I don't know if I did this right but any feedback or corrections would be greatly appreciated.. Thanks!
 
Physics news on Phys.org
You need to split up your tension into horizontal and vertical components. What forces are acting in the horizontal direction, the vertical? Then you can use Newton's second law to solve for the tension.
 

Similar threads

A father spins his child on a cart
  • · Replies 10 ·
Replies
10
Views
2K
Uniform Circular Motion, Find the Tension
  • · Replies 8 ·
Replies
8
Views
3K
Monkey accelerating up and down a rope
  • · Replies 38 ·
2
Replies
38
Views
5K
Finding the Tension in a Rope (Circular motion)
  • · Replies 6 ·
Replies
6
Views
4K
Tension on a Massive Rope: How to Calculate Tension at Different Points
  • · Replies 11 ·
Replies
11
Views
3K
Tension in a Rope from Lowering Down and Friction Braking Torque at Stop
  • · Replies 3 ·
Replies
3
Views
2K
Tension force of block and rope
  • · Replies 25 ·
Replies
25
Views
6K
Tension with circular motion on incline
  • · Replies 4 ·
Replies
4
Views
3K
Supposedly Simple Tension Problem
  • · Replies 4 ·
Replies
4
Views
4K
Momentum problem: 2 carts, finding initial speed
  • · Replies 13 ·
Replies
13
Views
6K