Question

Suppose a 60.0 , {kg} gymnast climbs a rope. (a) What is the tension in the rope if they climb at a constant speed? (b) What is the tension in the rope if they accelerate upward at a rate of 1.50 , {m/s}²?

1. The tension in the rope when the gymnast climbs at a constant speed is approximately:
a) 0 , {N}
b) 588 , {N}
c) 600 , {N}
d) 660 , {N}

Answer 1

The tension in the rope when the gymnast climbs at a constant speed is 588 N. When the gymnast accelerates upward at a rate of 1.50 m/s², the tension is approximately 678 N.

Step-by-step explanation:

To solve for the tension in the rope when the gymnast climbs, we apply Newton's second law of motion.

(a) Climbing at Constant Speed

When the gymnast climbs at a constant speed, the upwards force (tension) is equal to the force of gravity acting on the gymnast. Therefore, the tension T can be calculated using the formula T = m × g, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s²). For a 60.0-kg gymnast, the tension would be:

T = 60.0 kg × 9.81 m/s²

T = 588 N

(b) Accelerating Upward

If the gymnast accelerates upward at a rate of 1.50 m/s², the total force exerted on the rope is the sum of the force due to gravity and the force due to acceleration. Thus, the new tension T' is:

T' = m × (g + a)

Where a is the upward acceleration, 1.50 m/s². The new tension would be:

T' = 60.0 kg × (9.81 m/s² + 1.50 m/s²)

T' = 60.0 kg × 11.31 m/s²

T' = 678.6 N (which rounds down to 678 N when considering significant figures)