A cyclist is negotiating a circular track of radius 30 m. If the cyclist's speed
Practice Questions
Q1
A cyclist is negotiating a circular track of radius 30 m. If the cyclist's speed is 15 m/s, what is the net force acting on the cyclist if the mass of the cyclist is 60 kg?
180 N
120 N
90 N
60 N
Questions & Step-by-Step Solutions
A cyclist is negotiating a circular track of radius 30 m. If the cyclist's speed is 15 m/s, what is the net force acting on the cyclist if the mass of the cyclist is 60 kg?
Step 1: Identify the given values. The radius of the circular track (r) is 30 meters, the speed of the cyclist (v) is 15 meters per second, and the mass of the cyclist (m) is 60 kilograms.
Step 2: Write down the formula for centripetal force (F_c), which is F_c = mv²/r.
Step 3: Substitute the values into the formula. Replace m with 60 kg, v with 15 m/s, and r with 30 m.
Step 4: Calculate v² (15 m/s)², which equals 225 m²/s².
Step 5: Multiply the mass (60 kg) by v² (225 m²/s²). This gives 60 kg * 225 m²/s² = 13500 kg·m²/s².
Step 6: Divide the result by the radius (30 m). So, 13500 kg·m²/s² / 30 m = 450 kg·m/s².
Step 7: The result of the division is the centripetal force, which is 450 N.
Centripetal Force – The net force required to keep an object moving in a circular path, directed towards the center of the circle.
Newton's Second Law – The relationship between force, mass, and acceleration, which is fundamental in calculating net forces.
Circular Motion – The motion of an object in a circular path, which requires a constant inward force to maintain the circular trajectory.
