In a European country a bathroom scale displays its reading in kilograms. When a man stands on this scale, it reads 90.4 kg. When he pulls down on a chin-up bar installed over the scale, the reading decreases to 79.5 kg. What is the magnitude of the force he exerts on the chin-up bar?
The magnitude of the force he exerts on the chin-up bar is 10.9 kg.
To find the magnitude of the force exerted on the chin-up bar, we can use the concept of weight and Newton's second law of motion.
Step 1: Calculate the weight of the man when standing on the scale.
The reading on the scale when the man stands on it is 90.4 kg. This is the weight of the man since weight is the force exerted by gravity on an object. Therefore, the weight of the man is 90.4 kg.
Step 2: Calculate the weight of the man when pulling down on the chin-up bar.
The reading on the scale when the man pulls down on the chin-up bar is 79.5 kg. This is the weight of the man and the downward force exerted on the scale. Therefore, the weight of the man is 79.5 kg.
Step 3: Calculate the force exerted on the chin-up bar.
Since the man is exerting a force to pull down on the chin-up bar, this force can be calculated as the difference between the weight of the man when standing on the scale and the weight of the man when pulling down on the chin-up bar.
Force exerted = Weight when standing - Weight when pulling down
Force exerted = 90.4 kg - 79.5 kg
Force exerted = 10.9 kg
The magnitude of the force he exerts on the chin-up bar is 10.9 kg.
To find the magnitude of the force the man exerts on the chin-up bar, we need to consider the difference in readings on the bathroom scale, as it gives us an indication of the force exerted.
We know that the scale reading decreases from 90.4 kg to 79.5 kg when the man pulls down on the chin-up bar. This decrease in reading represents the decrease in the force exerted by the man's weight.
First, we need to find the difference in readings: 90.4 kg - 79.5 kg = 10.9 kg.
This difference in readings, 10.9 kg, corresponds to the reduction in the force the man is exerting. So, the magnitude of the force he exerts on the chin-up bar is 10.9 kg.
However, it's important to note that kilograms (kg) is a unit of mass, not force. To express the force in the correct unit, we need to convert the kg to newtons (N), which is the unit of force in the International System of Units (SI).
To convert kilograms to newtons, we can use the acceleration due to gravity, which is approximately 9.8 m/s². The formula to convert mass to force is F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity.
So, the magnitude of the force the man exerts on the chin-up bar is:
10.9 kg * 9.8 m/s² = 106.82 N (approximately)
Therefore, the man exerts a force of approximately 106.82 N on the chin-up bar.