A 1500 kg car drives around a flat 200-m-diameter circular track at 25m/s. What are the magnitude and direction of the net force on the car? What causes this force?
Answers
The correct answer to the question is : 9375 N.
CALCULATION:
As per the question, the mass of the car m = 1500 Kg.
The diametre of the circular track D = 200 m.
Hence, the radius of the circular path R =
=
= 100 m.
The velocity of the truck v = 25 m/s.
When a body moves in a circular path, the body needs a centripetal force which helps the body stick to the orbit. It acts along the radius and towards the centre.
Hence, the force acting on the car is centripetal force.
The magnitude of the centripetal force is calculated as -
Force F =
=
= 9375 N. [ANS}
The centripetal force is provided to the car in two ways. It is the friction which provides the necessary centripetal force. Sometimes friction is not sufficient. At that time, the road is banked to some extent which provides the necessary centripetal force.
Final answer:
The magnitude of the net force on the car is 9375 N, directed towards the center of the track. The net force is caused by the combination of the car's weight and the normal force of the road. These forces provide the necessary centripetal force to keep the car in its circular path.
Explanation:
The magnitude of the net force on the car can be calculated using the formula F = m×a, where m is the mass of the car and a is its acceleration. Since the car is moving in a circular path, its acceleration can be determined using the formula a = v^2/r, where v is the velocity of the car and r is the radius of the circular track. The direction of the net force is towards the center of the circular track, as it provides the necessary centripetal force to keep the car moving in a circular path.
Using the given values, the magnitude of the net force on the car is F = (1500 kg) × (25 m/s)^2 / (100 m) = 9375 N. The direction of the net force is towards the center of the circular track since it provides the centripetal force required to keep the car in its circular path.
The net force on the car is caused by two external forces: the weight of the car and the normal force of the road. The weight of the car acts vertically downwards, while the normal force of the road acts perpendicular to the surface. These two forces combine to provide the net force that keeps the car moving in a circular path.
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Answer: Here's my answer, I made it step-by-step so you can understand it! <3
Explanation:
To find the centripetal acceleration of the tip of the fan blade, we can use the formula for centripetal acceleration:
a = (v^2) / r
where:
a is the centripetal acceleration,
v is the linear velocity, and
r is the radius of the circular path.
Given that the fan completes 2 rotations every 1.0 second, we can find the angular velocity (ω) using the formula:
ω = (2π * n) / t
where:
ω is the angular velocity,
π is a constant (approximately 3.14),
n is the number of rotations (2),
and t is the time taken (1.0 second).
Substituting the values into the formula, we have:
ω = (2π * 2) / 1.0 = 4π rad/s
Next, we can calculate the linear velocity (v) using the formula:
v = r * ω
Substituting the given radius value (0.61 m) and the angular velocity we found earlier, we have:
v = 0.61 * 4π = 2.44π m/s
Finally, we can calculate the centripetal acceleration (a) using the formula:
a = (v^2) / r
Substituting the linear velocity and the radius, we have:
a = (2.44π)^2 / 0.61 = 5.88π^2 / 0.61 ≈ 96 m/s²
Therefore, the centripetal acceleration of the tip of the fan blade is approximately 96 m/s² (Option 4).
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