Student ties 0.060kg lead fishing weight to the end of a piece of string and whirls it around in a horizontal circle.if the radius of the circle is 0.30m and the object move with a speed of 2.0m/s..what is the horizontel component of d force that directs the lead weight towards the centre of the circle? What is the tension of the string??
centripetal and tension force= mv^2/r
it is a slight more complicated on tension: you have the horizontal centripetal force, and the weight at ninety degrees down. Add them as vectors.
To find the horizontal component of the force that directs the lead weight towards the center of the circle, you can use the centripetal force formula:
F = (m * v²) / r
Where:
F is the centripetal force
m is the mass of the lead weight
v is the velocity of the lead weight
r is the radius of the circle
Given:
m = 0.060 kg (mass of the lead weight)
v = 2.0 m/s (velocity of the lead weight)
r = 0.30 m (radius of the circle)
First, calculate the centripetal force:
F = (0.060 kg) * (2.0 m/s)² / 0.30 m
Simplify the equation:
F = 0.060 kg * 4.0 m²/s² / 0.30 m
Now, calculate:
F = 0.24 kg m²/s² / 0.30 m
Divide the units:
F = 0.80 kg m/s²
The horizontal component of the force that directs the lead weight towards the center of the circle is 0.80 kg m/s².
Now, to find the tension of the string, we need to consider the vertical component of the force. The vertical component is equal to the weight of the lead weight, which can be calculated using the formula:
Weight = m * g
Where:
Weight is the force due to gravity acting on the lead weight
m is the mass of the lead weight
g is the acceleration due to gravity (approximately 9.8 m/s²)
Given:
m = 0.060 kg (mass of the lead weight)
g = 9.8 m/s² (acceleration due to gravity)
Calculate the weight:
Weight = (0.060 kg) * (9.8 m/s²)
Weight = 0.588 kg m/s²
Since the tension in the string must balance the vertical force (weight), the tension in the string is also 0.588 kg m/s².
Therefore, the tension of the string is 0.588 kg m/s², and the horizontal component of the force that directs the lead weight towards the center of the circle is 0.80 kg m/s².