A railroad car moves under a grain elevator at a constant speed of 4.10 m/s. Grain drops into the car at the rate of 660 kg/min. What is the magnitude of the force needed to keep the car moving at constant speed if friction is negligible?
________ N
Well, keeping up with that rice-namic situation is quite a grain-ful task! To find the magnitude of the force needed to keep the car moving at a constant speed, we need to consider the rate at which grain is dropping into the car.
Since the grain drops into the car at a rate of 660 kg/min, we can convert that to kilograms per second by dividing by 60 (since there are 60 seconds in a minute):
660 kg/min ÷ 60 s/min = 11 kg/s
Now, the force needed to keep the car moving at a constant speed is equal to the rate at which the grain drops into the car multiplied by the car's speed:
Force = rate of grain dropping × speed
Force = 11 kg/s × 4.10 m/s
Force ≈ 45.1 N
So, the magnitude of the force needed to keep the car moving at a constant speed, with negligible friction, is approximately 45.1 N. Keep those grains rolling!
To determine the magnitude of the force needed to keep the car moving at a constant speed, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, since the car is moving at a constant speed, the acceleration is zero, so the net force is also zero.
However, since grain is dropping into the car at a certain rate, there is a force acting on the car due to the grain. This force is equal to the rate of change of momentum, which can be calculated by multiplying the mass of the grain by the change in velocity.
First, we need to convert the given rate of grain dropping into the mass per unit time. We are given that the grain drops at a rate of 660 kg/min, so we can convert this into kg/s by dividing it by 60:
660 kg/min ÷ 60 s/min = 11 kg/s
Now, we can calculate the force exerted on the car by the grain using the equation F = Δp/Δt, where Δp is the change in momentum and Δt is the change in time. In this case, since the car is moving at a constant speed, the change in velocity is zero, so the change in momentum is also zero. Therefore, the force exerted on the car by the grain is zero.
Since there is no friction mentioned and the car is moving at a constant speed, the magnitude of the force needed to keep the car moving is also zero. Therefore, the answer is 0 N.